1: The number of independent ways in which a mechanical system can move without violating any constraint is called
a. Constraint
b. Number of freedoms
c. Degrees of freedom
d. Generalized coordinates
2: The generalized momentum Pi need not always of linear momentum
a. Speed
b. Velocity
c. Dimension
d. None
3: A Single particle in a space requires three coordinates, so it has degree of freedom
a. Two
b. Three
c. Four
d. None
4: The sixth coordinates must satisfy a single constraints equation for a · · ·
a. Monoatomic
b. Diatomic
c. Triatomic molecule
d. None
5: In degree of freedom the · · · number of coordinates required to specify the configuration of a dynamical system
a. Minimum
b. Maximum
c. Both are correct
d. None
6: If constrains can be expressed as a function of position then it is called
a. Holonomic
b. Non Holonomic
c. Scleronomic
d. Neither
7: If constrains are stationary then it is called
a. Scleronomic
b. Non Holonomic
c. Rheononomic
d. All of these
8: First difficulty of constraints in the solution of mechanical problems
a. Force of constraints
b. Coordinates ri , d are not all independent
c. None of these
d. Both ‘a’ and ‘b’
9: Rigid body and gas molecules within the wall of container are example of
a. Holonomic constraints
b. Non Holonomic constraints
c. constraints
d. All of these
10: The square of the period is proportional to semi major axis of
a. cubic orbit
b. vertical orbit
c. central orbit
d. Elliptical orbit
11: Further away from planet is from sun · · · it takes what period reaches orbit to sun
a. Longer
b. shorter
c. None
d. Undefined
12: The area per unit time swept out by a radius vector from sun to planet becomes
a. Constant
b. independent
c. vertical
d. none of these
13: Planets move in · · ·. Around sun
a. Elliptical orbits
b. Cubic orbits
c. Central orbits
d. Horizontal axis
14: the angular momentum of rigid body is L and its K.E is halved. What happens to its angular momentum
a. L
b. 2L
c. L/2
d. L/4
15: If a linear momentum is increased by 50% K.E will increase by what percent?
a. 25%
b. 50%
c. 100%
d. 125%
16: The gravitational force between two masses is
a. Repulsive
b. Attractive
c. Zero
d. Infinity
17: The value of universal gravitational constant G is
a. 4 × 1042 Nm2/Kg2
b. 6.67 × 1011Nm2/Kg2
c. 9.81 cm/sec2
d. 6.67 × 10−11Nm2/Kg2
18: The angular momentum is in a central force field
a. Zero
b. Not conserved
c. infinity
d. conserved
19: The areal velocity of the particle in a central force field is
a. Zero
b. constant
c. infinity
d. Not conserved
20: At the turning point in an arbitrary potential field the radial velocity is
a. Zero
b. 1
c. infinity
d. 1/2
21: For hyperbolic orbit the values of energy E and eccentricity ϵ are
a. E = 0 and ϵ = 1
b. E > 0 and ϵ > 1
c. E > 0 and ϵ = 1
d. E> 0 and ϵ = 0
22: For parabolic orbit the values of energy E and eccentricity ϵ are
a. E = 0 and ϵ = 1
b. E > 0 and ϵ > 1
c. E > 0 and ϵ = 1
d. E > 0 and ϵ = 0
23: For elliptical orbit the values of energy E and eccentricity ϵ are
a. E = 0 and ϵ > 1
b. E > 0 and ϵ > 1
c. E < 0 and ϵ < 1
d. E > 0 and ϵ = 0
24: For circular orbit the value of eccentricity
a. ϵ > 1
b. ϵ ≥ 1
c. ϵ < 1
d. ϵ = 0
25: All the planet moves around the Sun in orbit
a. circular
b. parabolic
c. hyperbolic
d. elliptical
26: In the formation of the cycloidal curves, the circle which rolls with a fixed point without
slipping is called
a. Generating circle
b. Rolling circle
c. Slipping circle
d. Direct circle
27: · · · is a curve generated by a point on the circumference of a circle, which rolls without
slipping along another circle outside it
a. Trochoid
b. Epicycloid
c. Hypotrochoid
d. Involute
28: Type of curve is created by the intersection of a plane parallel to the side of cone?
a. Parabola
b. Hyperbola
c. Ellipse
d. Roulette
29: Type of curve is created by the intersection of a plane with a cone which makes an angle with the axis greater than the angle between the side of the cone and the axis?
a. Parabola
b. Hyperbola
c. Ellipse
d. Roulette
30: Curve generated by a point on the circumference of a circle, which rolls without slipping along outside of another circle is known as
a. Hypocycloid
b. Epicycloid
c. Cycloid
d. Trochoid
31: Curved traced out by a point which moves uniformly both about the center and at the same time away or towards the center is known as
a. Involute
b. Archimedean spiral
c. Cycloid
d. None of above
32: Poisson bracket is used to define a?
a. Poisson function
b. Poisson equation
c. Poisson algebra
d. None of the above
33: The Poisson bracket is an important binary operation in
a. Hamiltonian mechanics
b. lagrangian formalism
c. both a & b
d. None of the above
34: Hamilton’s formulation of classical mechanics made use of a mathematical tool called
a. angular momentum
b. Poisson brackets
c. None of the above
d. lagrange
35: the bracket of p with any reasonably smooth function of q is
a. [p, f(a)] = df/dq
b. [p, f(q)] = da/dq
c. [p, f(q)] = df/fq
d. [p, f(q)] = df/dq
36: Lagrange’s bracket is
a. Canonical invariant
b. Non-invariant
c. Canonical variant
d. None of these
37: Poisson’s bracket is
a. invariant under canonical transformation
b. variant under canonical transformation
c. Both a and b
d. None of these
38: As there are three generalized coordinates, then Hamilton’s canonical equations will be · · · in number
a. Three
b. Four
c. Five
d. Six
39: The generalized momentum is also called
a. conjugate momentum
b. canonical momentum
c. Both a and b
d. None of these
40: Which of the following answer is true for the Lagrange’s bracket
a. -1
b. 0
c. 1
d. 2
41: If the Poisson bracket of a function with the Hamiltonian vanishes
a. the function depends upon time
b. the function is a constant of motion
c. the function is not the constant of motion
d. None of these
42: If we make a canonical transformation from the set of variables (pk, qk) to new set of Variables (Pk, Qk) and the transformed Hamiltonian is identically zero, then
a. the new variables are constant in time
b. the new variables are not constant in time
c. the new variables are not cyclic
d. None of these
43: Hamiltonian H is defined as
a. the total energy of the system
b. the difference in energy of the system
c. the product of energy of the system
d. All of these
44: Whenever the Lagrangian for a system does not contain a coordinate explicitly.
a. pk is cyclic coordinate
b. pk the generalized momentum is a constant of motion
c. qk is always zero
d. None of these
45: The dimensions of generalized momentum
a. are always those of linear momentum
b. may be those of angular momentum
c. may be those of linear momentum
d. Both b and c are true
46: If the Lagrangian does not depend on time explicitly
a. the Hamiltonian is constant
b. Hamiltonian not constant
c. the kinetic energy is constant
d. the potential energy is constant
47: Any · · · on the freedom of movement of a system of particles in the form equation is
called Constraints
a. Restrictions
b. Points
c. Both
d. resistance
48: Example of the Constraints is
a. Rigid bodies
b. a particle on the surface
c. A bead of abacus
d. all
49: In the Constraints the particles can move
a. On the surface
b. in the surface
c. Over the surface
d. none
50: There are only · · · types of constraints
a. One
b. two
c. Three
d. four
51: The constraints which can be expressed as a function of positions and time are called
a. Holonomic
b. Non holonomic
c. Both
d. rheonomic
52: Example of the Scleronomic constraints
a. Pendulum
b. rigid body
c. Particles on the surface of solid sphere
d. Beads of abacus
53: If the Constraints depends on time explicitly then it is called
a. Rheonomic
b. Scleronomic
c. Non holonomic
d. None
54: The constraints which cannot be expressed as a function of position and time are called
a. Non holonomic
b. Rehonomic
c. Scleronomic
d. none
55: In Lagrangian approach, the flow parcels follows
a. Pressure field
b. Velocity field
c. Temperature field
d. Density field
56: Each parcel in the Lagrangian formulation is tagged using
a. Time-dependent position vector
b. Time -independent position vector
c. Time-dependent velocity vector
d. Time-independent velocity vector
57: Which of these is an acceptable tag for Lagrangian parcels?
a. Parcels center of mass at instantaneous time
b. Parcels center of pressure at instantaneous time
c. Parcels center of mass at initial time
d. Parcels center of pressure at initial time
58: The Lagrangian equation of motion is order differential equations.
a. First
b. Second
c.Third
d. Forth
59: In Lagrange’s equation virtual displacement does not involve
a. Space
b. Time
c. N number of particle
d. None
60: In Lagrange’s equation if there are N number of particle and so the generalized coordinated are
a. n = N − K
b. n = 3N
c. n = 3N − K
d. n = 3n − k
61: In a simple one-constraints Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function.
a. True
b. False
c. None
d. May be true
62: Whenever the Lagrangian for a system does not contain a coordinate explicitly
a. Pk is cyclic coordinates
b. Pk the generalized momentum is a constant of motion
c. qk is always zero
d. None of these
63: Euler equation govern flows
a Viscous adiabatic flows
b Inviscid flows
c. Adiabatic and inviscid flow
d. Adiabatic flows
64: In Euler form of energy equations, which of these terms is not present?
a. Rate of charge of energy
b. Heat radiation
c. Heat source
d. Thermal conductivity
65: The gravitational force between two masses is
a. Repulsive
b. Attractive
c. Zero
d. Infinite
66: All the planet moves around the sun in orbit?
a. Circular
b. Parabolic
c. Elliptical
d. Hyperbolic
67: The combination of total and partial derivative that enters into Euler equation is called
a. Variations derivative
b. Degree of freedom
c. Actual length
d. None of these
68: One of the possible paths systems will travel through a path which is
a. Long
b. Shorter
c. Stationary
d. None of these
69: A particle of unit mass moves in a potential $V (x) = ax^2+\frac{b}{x^2}$ , where a and b are positive constants. The angular frequency of small oscillation about the minimum of the potential
a. $\sqrt{8b}$
b. $\mathbf{\sqrt{8a}}$
c. $\sqrt{\frac{8a}{b}}$
d. $\sqrt{\frac{8b}{a}}$
70: The acceleration due to gravity (g) on the surface of Earth is approximately 2.6 times that on the surface of Mars. Given that the radius of Mars is about one half the radius of Earth, the ration of the escape velocity on Earth to that on Mars is approximately
a. 1.1
b. 1.3
c. 2.3
d 5.2
71: A constant force F is applied to a relativistic particle of rest mass m. If the particle starts from rest at t = 0, its speed after time t is
a. $\frac{Ft}{m}$
b. $c\tan h(\frac{Ft}{mc})$
c. $c(1-e^{-\frac{Ft}{mc}})$
d. $\mathbf{\frac{Fct}{\sqrt{F^2t^2+m^2c^2}}}$
72: The potential of a diatomic molecule as a function of the distance r between the atoms is given by $\mathbf{V (r) = -\frac{d}{r^6}+\frac{b}{r^{12}}}$. The value of the potential at equilibrium separation between the atom is
a. $-\frac{4a^2}{b}$
b. $-\frac{2a^2}{b}$
c. $-\frac{a^2}{2b}$
d. $\mathbf{-\frac{a^2}{4b}}$
73: Two particles of identical mass moves in circular orbits under a central potential $\mathbf{V\left(r\right)=\frac{1}{2}kR^2}$. Let l1 and l2 be the angular momenta and r1 and r2 be the radii of the orbits respectively. If $\frac{l_1}{l_2} = 2$. the value of r1/r2 is
a. $\sqrt\mathbf{2}$
b. $\frac{1}{\sqrt2}$
c. 2
d. 1/2
74: A planet of mass m moves in the inverse square central force field of the sun of mass M. If the semi-major and semi-minor axes of the orbit are a and b, respectively, the total energy of the planet is
a. $\mathbf{-\frac{GMm}{a+b}}$
b. $-GMm(\frac{1}{a}+\frac{1}{b})$
c. $-\frac{GMm}{a+b}(\frac{1}{b}-\frac{1}{a})$
d. $-GMm(\frac{a-b}{\left(a+b\right)^2})$
75: An annulus of mass M made of a material of uniform of uniform density has inner and outer radii a and b respectively. Its principle moment of inertia along the axis of symmetry perpendicular to the plane of the annulus is
a. $\frac{1}{1}M\frac{(b^4+a^4)}{b^2-a^2}$
b. $\frac{1}{2}M\pi(b^2-a^2)$
c. $\frac{1}{\ 2}M(b^2-a^2)$
d. $\mathbf{\frac{1}{2}M(b^2+a^2)}$
76: Two events separated by a (spatial) distance 99 m, are simultaneous in one inertial frame. The time interval between these two events is a frame moving with a constant speed 0.8 c (where speed of light c = 3 × 108 m/s) is
a. 60 s
b. 40 s
c. 20 s
d. 0 s
77: If the Lagrangian of a particle moving in one dimension is given by L = x2/2 − V (x) the Hamiltonian is
a. $\mathbf{\frac{1}{2}xp^2+V(x)}$
b. $\frac{x^2}{2x}+V(x)$
c. $\frac{1}{2}x^2+V(x)$
d. $\frac{p^2}{2x}+V(x)$
78: A horizontal circular platform mutes with a constant angular velocity Ω directed vertically upward. A person seated at the center shoots a bullet of mass m horizontally with speed v. The acceleration of the bullet, in the reference frame of the shooter, is
a.2vΩ to his right
b. 2vΩ to his left
c. vΩ to his right
d. vΩ to his left
79: The Poisson bracket ${\left|\vec{r}\right|,|\vec{p|}}$ has the value
a. $\left|\vec{r}\right|,|\vec{p|}$
b. $\mathbf{\hat{r}.\hat{p} }$
c. 3
d. 1
80: What is proper time interval between the occurrence of two events i f in one inertial frame events are separated by 7.5 × 108 m and occur 6.5 s apart?
a. 6.50 s
b. 6.00 s
c. 5.7 s
d. 5.00 s
81: A solid cylinder of height H, radius R and density ρ, floats vertically on the surface of a liquid of density ρ◦. The cylinder will be set into oscillatory motion when a small instantaneous downward force is applied. The frequency of oscillation is
a. $\frac{\rho g}{\rho_oH}$
b. $\frac{\rho}{\rho_o}\sqrt{\frac{g}{H}\ }$
c. $\sqrt{\frac{\rho g}{\rho_oH}}$
d. $\mathbf{\sqrt{\frac{\rho_og}{\rho H}}}$
82: Two bodies of equal mass m are connected by a massless rigid rod of length l lying in the xy−plane with the center of the rod at the origin. If this system is rotating about the z−axis with a frequency ω, its angular momentum is
a. $\frac{ml^2\omega}{4}$
b. $\mathbf{\frac{ml^2\omega}{2}}$
c. $ml^2\omega$
d. $2ml^2\omega$
83: The muon has mass 105 MeV/c2 and mean lifetime 2.2 µs in its frame. The mean distance traversed by a muon of energy 315 MeV before decaying is approximately
a. 3 × 105 km
b. 2.2 cm
c. 6.6 µm
d. 1.98 km
84: A planet of mass m and an angular momentum L moves in a circular orbit in a potential, $V(r) =-\frac{k}{r},$, where k is a constant. If it is slightly perturbed radially, the angular frequency of radial oscillation is
a. $\frac{mk^2}{\sqrt2L^3}$
b $\frac{mk^2}{L^3}$
c. $\frac{\sqrt2mk^2}{L^3}$
d. $\frac{\sqrt3mk^2}{L^3}$
85: The number of degrees of freedom of a rigid body in d space-dimension is
a. 2 d
b. 6
c. $\mathbf{\frac{d\left(d+1\right)}{2}}$
d. d!
86: Let A, B and C be function of phase space variables (coordinates and momenta of a mechanical system). If {◦} represents the Poisson bracket, the value of {A, {B, C}} – {{A, B}, C} is given by
a. 0
b. {B, {C, A}}
c. {A, {C, B}}
d. {{C, A}, B}
87: A particle moves in a potential V = x2 + y2 + z2/2 . Which components(c) of the angular momentum is/are constant(s) of motion?
a. None
b. Lx, Ly and Lz
c. only Lx and Ly
d only Lz
88: A particle of mass m and coordinate q has the Lagrangian $L =\frac{1}{2}mq^2-\frac{\lambda}{2}qq^2$, where λ is a constant. The Hamiltonian for the system is given by
a. $\frac{p^2}{2m}+\frac{\lambda q p^2}{2m^2}$
b. $\frac{p^2}{2(m-\lambda q)}$
c. $\frac{p^2}{2m}+\frac{\lambda q p^2}{2\left(m-\lambda q\right)^2}$
d. $\frac{pq}{2}$˙
89: A canonical transformation relates the old coordinates (q, p) to the new ones (Q, P) by the relation Q = q2 and P = pq/2. The corresponding time independent generating function is
a. $\frac{p}{q^2}$
b. $\mathbf{q^2P}$
c. $\frac{q^2}{P}$
d. $qP^2$
90: The radius of Earth is approximately 6400 km. The height h at which the acceleration due to Earth’s gravity differs from g at the Earth’s surface by approximately 1% is
a. 64 km
b. 48 km
c. 32 km
d. 16 km
91: The Hamiltonian of a classical particle moving in one dimension is $H = \frac{p^2}{2m}+\alpha q^4$ where α is a positive constant and p and q are its momentum and position respectively. Given that its total energy $E\le E_o$ the available volume of phase space depends on Eο as
a. $\mathbf{E_o^{34}}$
b. E◦
c. $\sqrt E_o$
d. is independent of E◦
92: A mechanical system is described by the Hamiltonian $H (q, p) =\frac{p^2}{2m}+\frac{1}{2}m\omega^2q^2$. As aresult of the canonical transformation generated by $F (q.Q) = -\frac{Q}{a}$, the Hamiltonian in the new coordinate Q and momentum P becomes
a. $\frac{1}{2m}Q^2P^2+\frac{m\omega^2}{2}Q^2$
b.$\frac{1}{2m}Q^2P^2+\frac{m\omega^2}{2}P^2$
c. $\frac{1}{2m}P^2+\frac{m\omega^2}{2}Q^2$
d. $\mathbf{\frac{1}{2m}Q^2P^4+\frac{m\omega^2}{2}P^{-2}}$
93: A particle moves in two dimensions on the ellipse $\mathbf{x^2\ +\ 4y^2\ =\ 8}$. At a particular instant it is at the point (x, y) = (2,1) and the x-component of its velocity is 6 (in suitable units). Then the y−component of its velocity is
a. −3
b. −2
c. 1
d. 4
94. Consider three inertial frames of reference A, B and C. The frame B moves with a velocity c/2 with respect to A, and C moves with a velocity c/10 with respect to B in the same direction. The velocity of C as measured in A is
a. 37c
b. 47c
c. 7c
d. √73c
95: If the Lagrangian of a dynamical system in two dimensions is $L\ =\ \frac{1}{2}m{\dot{x}}^2\ +\ m\dot{x}\dot{y}$˙, then its Hamiltonian is
a. $H=\frac{1}{m}P_xP_y+\frac{1}{2m}P_y^2$
b. $H=\frac{1}{m}P_xP_y+\frac{1}{2m}P_x^2$
c. $\mathbf{H=\frac{1}{m}P_xP_y-\frac{1}{2m}P_y^2}$
d. $\frac{1}{m\ }P_xP_y-\frac{1}{2m}P_x^2$
96: A particle of mass m moves in the one-dimensional potential $V\ \left(x\right)=\frac{\alpha}{3}x^3\ +\frac{\beta}{4}x^4$, where α, β > 0. One of the equilibrium points is x=0 . The angular frequency of small oscillation about the other equilibrium point is
a. $\frac{2\alpha}{\sqrt{3m\beta}}$
b. $\frac{\alpha}{\sqrt{m\beta}}$
c. $\frac{\alpha}{\sqrt{12m\beta}}$
d. $\frac{\alpha}{\sqrt{24m\beta}}$
97: A particle of unit mass moves in the xy−plane in such a way that ˙ x(t) = y(t) and y˙(t) = -x(t). We can conclude that it is in a conservative force-field which can be derived from the potential
a. $\mathbf{\frac{1}{2}(x^2+y^2)}$
b. $\frac{1}{2}(x^2-y^2)$
c. x+y
d. x-y
98: Consider a particle of mass m moving with a speed v. If TR denotes the relativistic kinetic energy and TN its non-relativistic approximation, then the value of $\frac{T^R-T^N\ }{{T_T}_R}$ for v =0.01 c, is
a. $1.25\ \times\ {10}^{-5}$
b. $5.0\ \times\ {10}^{-5}$
c. $7.5\ \times\ {10}^{-5}$
d. None of these
99: A particle in two dimension is in a potential V (x, y) = x+2y . Which of the following (apart from the total energy of the particle) is also a constant of motion?
a. $\mathbf{p_y\ -\ 2p_x}$
b.$p_x\ -\ 2p_y$
c. $p_x\ +\ 2p_y$
d. $p_y\ +\ 2p_x$
100: After a perfectly elastic collision of two identical balls, one of which was initially at rest, the velocities of both of the balls ar e non-zero. The angle θ the final, velocities (in the lab frame) is
a. $\theta=\frac{\pi}{2}$
b. $\theta=\pi$
c. $0<\ \theta\le\frac{\pi}{2}$
d. $\frac{\pi}{2}<\ \theta\ \le\ \pi$
101: The total angular momentum of system of particles is constant if:
a. Total force is zero
b. Total energy is zero
c. Total torque is zero
d. Total momentum is zero
102: The ……….. force deflects air in the northern hemisphere to right producing cycloid motion:
a. Centripetal
b. Coriolis
c. Euler
d. Electric
103: Acceleration of an object depends on:
a. Force
b. Mass
c. a & b
d. Unpredictable
103: For a system of many particles the kinetic energy consists of:
a. One part
b. Two parts
c. Three parts
d. Many parts
104: Gravitational force is:
a. Central force
b. Attractive force
c. Conservative
d. All of these
105: If total external force is zero then total linear momentum is:
a. Zero
b. Conserved
c. Maximum
d. Minimum
106: The sum of all external forces on a system of many particles is zero. Which of the following must be true for the system:
a. Total mechanical energy is constant
b. Total linear momentum is constant
c. Total potential energy is constant
d. Total kinetic energy is constant
107: If work done is independent of path followed then force is:
a. Frictional
b. Non-conservative
c. Conservative
d. Imaginary
108: Everybody continues to be in a state of rest or of uniform motion in a straight line unless it is compelled by an external force. this statement is called:
a. Newton’s 3rd law of motion
b. Newton’s 2nd law of motion
c. Newton’s 1st law of motion
d. Newton’s law of gravitation
109: Newton’s laws are valid in:
a. Inertial frame
b. Non inertial frame
c. a & b
d. None
109: The branch of physics which deals with ordinary materials is called:
a. Quantum
b. Classical
c. Solid state physics
d. Condensed matter
110: If forces acting on a particle are conservative then:
a. $T+V=0$
b. $L+T=0$
c. $T+V=constant$
d. $L-T=constant$
111: Angular momentum is given by:
a. $L=m_i\left(rv\right)$
b. $\mathbf{m_i\left(r_i\times v_i\right)}$
c. $L=m_i(r_i+v_i)$
d. $L=m_fv_f-m_iv_i$
112: Rate of change linear momentum gives:
a. Impulse
b. Torque
c. Force
d. Velocity
113: A particle of mass M moving with speed v collides with a stationary particle of equal mass. After collision both particles move. Let β be the angle between two velocity vectors. If collision is inelastic then:
a. β is always equal to 90o
b. β is always less than 90o
c. β is always greater than 90o
d. Insufficient data to calculate
114: Newtonian mechanics is not applicable to:
a. Particles moving with speed of light
b. Particles moving with speed comparable to speed of light
c. Objects of atomic size
d. All of these
115: For conservative force:
a. $\oint_{C}\vec{F}.d\vec{r}=0$
b. $\vec{\nabla}\times\vec{F}=0$
c. a & b
d. Cannot be answered
116: Newton’s 1st law of motion is applicable to only:
a. Bound particles
b. Free particles
c. a & b
d. None
117: A body keeps moving once set in motion. This property is called:
a. Momentum
b. Force
c. Inertia
d. Torque
118: A particle of mass M moving with speed v collides with a stationary particle of equal mass. After collision both particles move. Let β be the angle between two velocity vectors. If collision is inelastic then:
a. β is always equal to 90o
b. β is always less than 90o
c. β is always greater than 90o
d. Insufficient data to calculate
119: A body is moving in a straight line by a machine delivering constant power. The distance d moved by body in time t is:
a. $t^\frac{1}{2}$
b. $\mathbf{t^\frac{3}{2}}$
c. $t^2$
d. $t^\frac{3}{4}$
120: A tube of length l is completely filled with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by liquid at the other end is:
a. $F=m\omega^2l$
b. $F=\frac{1}{2}m\omega^2l$
c. $\mathbf{F=\frac{1}{4}m\omega^2l }$
d. $\frac{1}{2}m\omega^2l^3$
121: Mutual interaction force between two particles can change:
a. Linear momentum but not kinetic energy
b. Linear momentum as well as kinetic energy
c. Kinetic energy but not linear momentum
d. All of these
122: Angular momentum of particles is defined as:
a. Kinetic energy
b. Linear momentum
c. Torque
d. Mass
123: The work energy theorem states that the work done is equal to the change in:
a. Potential energy
b. Kinetic energy
c. Torque
d. Force
124: Rate of change of angular momentum is called:
a. Linear momentum
b. Force
c. Torque
d. Impulse
125: Forces of constraints do ………… work for principle of virtual work done:
a. Negative
b. Positive
c. Zero
d. Maximum
126: Constraints that can be expressed as equations of coordinates and time i.e. $f\left(r_1,r_2,r_3,\ldots\ldots r_N,t\right)=0$ are said to be:
a. Holonomic
b. Non-Holonomic
c. Cruciform
d. Simple
127: Lagrangian is a ………. Quantity:
a. Vector
b. Scalar
c. Dyadic
d. All of these
128: Lagrange is a function of:
a. Variable energies
b. Conserved energies
c. Difference of energies
d. Sum of energies
129: The term $Q_j=\sum_{i}{F_i^a.\frac{\partial r_i}{\partial q_i}}$ is called:
a. Generalized work
b. Generalized force
c. Force
d. Virtual work
130: Generalized displacement of a rigid body is represented by …….. motion:
a. Vibrational
b. Rotational
c. Translational
d. a & c
131: Lagrangian is a function of:
a. Generalized coordinates
b. Generalized velocity
c. Time
d. All of these
132: A rigid body is moving in space has degree of freedom:
a. Three
b. Five
c. Nine
d. Six
133: Constraints of rigid body has:
a. Holonomic
b. Rheonomic
c. Scleronomic
d. a & c
134: Generalized coordinates are:
a. Necessarily spherical coordinates
b. Necessarily Cartesian coordinates
c. Depend on each other
d. Independent of each other
135: A particle constrained to move along any curve is an example of:
a. Non-holonomic constraints
b. Holonomic constraints
c. Isolated constraints
d. Scleronomic constraints
136: In case of Atwood machine the number of independent coordinates are:
a. 2
b. 4
c. 3
d. 1
137: At equilibrium the virtual work of applied force is:
a. Maximum
b. Zero
c. Minimum
d. None
138:The degrees of freedom of spherical pendulum is:
a. 2
b. 4
c. 3
d. 1
139: In case of simple pendulum the number of independent coordinates are:
a. 1
b. 4
c. 3
d. 2
140: Configuration space is also known as:
a. 3N-dimensional space
b. 2N-dimesnional space
c. N-dimensional space
d. None
141: If a particle is constrained to move on surface the force of constraint is then:
a. Perpendicular to surface
b. Parallel to surface
c. Antiparallel to surface
d. Tangent to surface
142: A system is in equilibrium if total work done by the applied force is zero then it is called
a. Principle of virtual work
b. Hamiltonian’s principle
c. Principle of static equilibrium
d. None
143: The constraint on a bead on a uniformly rotating wire in a force free space is:
a. Scleronomic
b. Holonomic
c. Rheonomic
d. All of these
144: If generalized coordinate is ![]()
then corresponding generalized force has dimensions of:
a. Energy
b. Torque
c. Momentum
d. Impulse
145: If generalized coordinate has dimension of velocity then generalized velocity has the dimensions of:
a. Force
b. Displacement
c. Acceleration
d. Momentum
146: The number of independent coordinates required to described a system are called:
a. Generalized coordinates
b. Cartesian coordinates
c. a & b
d. None
147: Generalized coordinates are:
a. Dependent quantity
b. Independent quantity
c. Measurable quantity
d. None
148: D’ Alembert principle states that a dynamic system is in equilibrium if virtual work done by the actual force plus reverse effective force is :
a. Negative
b. Positive
c. Zero
d. Maximum
149: Any set of parameters that can be conveniently used to specify the configuration of system are called as:
a. Configuration space
b. Generalized coordinates
c. Position coordinates
d. None
150: Principle of virtual work is valid for:
a. Sliding motion
b. Rolling contact with slipping
c. Frictionless surface
d. a & b
151: For D’ Alembert principle constraint force is……… to virtual displacement :
a. Parallel
b. Perpendicular
c. Equal
d. Antiparallel
152: A particle constrained to move along the inner surface of a fixed hemispherical bowl. The number of degrees of freedom of particle is:
a. Three
b. One
c. Two
d. Unknown
152: The shortest distance between two points in space will be:
a. Parabola
b. Catenary
c. Straight line
d. Circle
153: A usual expression for the conserved angular momentum in central force problem is:
a. $l=mr^2\theta$
b. $\mathbf{ l=mr^2\dot{\theta}}$
c. $l=mr^2\theta^2$
d. $l=mr^2{\dot{\theta}}^2$
154: The derivation of Euler-Lagrange equation is a problem of:
a. Differentiation
b. Integration
c. Calculus of variation
d. All of these
154: The homogeneity of time leads to law of conservation of:
a. Angular momentum
b. Linear momentum
c. Energy
d. Parity
155: Choose the correct statement:
a. In ∆-variation, time as well as position coordinates are allowed vary
b. $\delta-variation$ dose not involves time
c. a & b
d. None
156: Conservation of areal velocity ………………. For planetary motion only
a. Limited case
b. Unlimited case
c. Holds
d. None
157: A particle is moving under central force about a fixed center of force. Choose the correct statement:
a. Motion of particle is always on circular path
b. Its angular momentum is conserved
c. Motion of particle takes place in plane
d. b & c
158: Central force is:
a. Infinite
b. Conservative
c. Non-conservative
d. None
159: Area covered by planet in equal intervals of time is:
a. Variable
b. Constant
c. Zero
d. Stationary
160: In planetary motion orbits are elliptical with axis:
a. Central axis
b. Perpendicular axis
c. Major axis and minor axis
d. All of these
161: Force between Sun and Planet is:
a. Electrostatic force
b. Gravitational force
c. Electromagnetic force
d. None
162: Two particles of masses m and 2m interacting via gravitational force are rotating about common center of mass with angular velocity w at a fixed distance r. If the particle of mass 2m is taken at origin O. Then
a. The force between them can be represented by $F=\mu\omega^2r$
b. In the inertial frame the origin $O$ is moving on a circular path of radius $\frac{r}{3}$
c. a & b
d. None of these
163: In central force problem, the conservation of angular momentum is equivalent to saying that:
a. Total energy is constant
b. Linear momentum is constant
c. Effective potential is constant
d. Areal velocity is constant
165: The force of attraction between Sun and planet is a central force and is given by:
a. Coulomb’s law
b. Newton’s 2nd law
c. Gravitational law
d. Kepler’s law
166: The ratio of number of particles scattered into solid angle per unit time per incident intensity is known as:
a. Cross-section of scattering
b. Scattered particle length
c. Solid angle
d. Radian
167: A particle is moving on elliptical path under inverse square law force of form $f\left(r\right)=-\frac{k}{r^2}$. The eccentricity of orbit is:
a. Function of total energy
b. Function of angular momentum
c. a & b
d. Independent of angular momentum
168: In the Rutherford scattering formula both incident and target were:
a. Negative charge
b. Same charge
c. Positive charge
d. Opposite charge
169: The force due to deflection of body is called:
a. Pseudo force
b. Coriolis force
c. Deflecting force
d. Apparent force
170: The maximum and minimum velocities of a satellite are $v_1$ and $v_2$ respectively. The eccentricity of orbit of satellite is:
a. $e=\frac{v_1}{v_2}$
b. $e=\frac{v_2}{v_1}$
c. $e=\frac{v_1+v_2}{v_1-v_2}$
d. $e=\frac{v_1-v_2}{v_1+v_2}$
171: The areal velocity of planet remains constant is known as Kepler’s :
a. 1st law
b. 2nd law
c. 3rd law
d. None
172: The value of eccentricity for an elliptical orbit is:
a. $e=\frac{v_1-v_2}{v_1+v_2}$
b. $\in=1$
c. $\in=0 $
d. $\mathbf{0}<\in<\mathbf{1}$
173: Rutherford differential cross-section has dimensions of:
a. Solid angle
b. Area
c. Length
d. Volume
174: Kepler’s 2nd law of planetary motion directly follows from:
a. Homogeneity of time
b. Homogeneity of space
c. Law of conservation of angular momentum
d. Law of conservation of linear momentum
175: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This statement is called:
a. Kepler’s 1st law
b. Kepler’s 2nd law
c. Kepler’s 3rd law
d. None
176: Consider a comet of mass ![]()
moving in a parabolic orbit around the Sun. The closest distance between the comet and Sun is ![]()
, the mass of Sun is ![]()
and the universal gravitational constant is ![]()
. The angular momentum of comet is:
a. $\mathbit{m}\sqrt{\mathbf{2}\mathbit{GMs}}$
b. $M\sqrt{2Gms} $
c. $s\sqrt{GmM}$
d. $G\sqrt{Mms}$
177: A minimum distance of incident particle from the target nucleus at which incident particle is scattered considerably is known as:
a. Radial distance
b. Impact parameter
c. Transverse distance
d. None
178: In motion under central force which of the following is true:
a. Acceleration is constant
b. Linear momentum is conserved
c. Angular momentum is conserved
d. All of these
179: The Lagrangian for Sun-Earth system is:
a. $\mathbf{L}=\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{\dot{\mathbf{r}}}^\mathbf{2}+\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{\dot{\mathbf{r}}}^\mathbf{2}{\dot{\mathbf{\theta}}}^\mathbf{2}+\frac{\mathbf{GMm}}{\mathbf{r}}$
b. $L=\frac{1}{2}m{\dot{r}}^2+\frac{1}{2}m{\dot{r}}^2{\dot{\theta}}^2-\frac{GMm}{r}$
c. $L=\frac{3}{2}m{\dot{r}}^2+\frac{GMm}{r}$
d. $L=\frac{1}{2}m{\dot{r}}^2{\dot{\theta}}^2-\frac{GMm}{r}$
180: In Rutherford scattering experiment the path of scattered particle is:
a. Parabola
b. Hyperbola
c. Ellipse
d. Straight line
189; A system with respect to which centre of mass of a particle is at rest is called:
a. Laboratory coordinate system
b. Cartesian coordinate system
c. Centre of mass coordinate system
d. Polar coordinate system
190: If a particle is moving under a potential of form $V\left(r\right)=-\frac{k}{r}$ then trajectory made by particle is a:
a. Helix
b. Great circle
c. Straight line
d. Conic section
191: A system that possesses …………. Symmetry, conserve angular momentum:
a. Translational
b. Spherical
c. Space reflection
d. Time reversal
192: Canonical equations of motion represent ……… relations:
a. $n$
b. $\mathbf{2n}$
c. n+1
d. 2n+1
193: Hamilton’s equations of motion are…….. equations:
a. Linear
b. Quadratic
c. 1st order differential
d. 2nd order differential
194: Poisson brackets play the same role in classical mechanics as ………. Play in quantum mechanics:
a. Commutation relations
b. Operator
c. Wave function
d. Probability
195: Jacobi identity and anti-symmetry property of Poisson brackets together define:
a. Linear Algebra
b. Lagrangian formalism
c. Hamiltonian formalism
d. None
196: The product of generalized coordinates and its conjugate momentum has dimensions of:
a. Angular momentum
b. Linear momentum
c. Energy
d. Force
197: Hamilton function can be represented by:
a. $f\left(V,p,t\right)$
b. $\mathbf{f}\left(\mathbf{p},\mathbf{q},\mathbf{t}\right)$
c. $f\left(q,p,t\right)$
d. $f(c,V,t)$
198: The Lagrangian of a particle moving in a plane under the influence of a central potential is given by $L=\frac{1}{2}m\left({\dot{r}}^2+r^2{\dot{\theta}}^2\right)-V\left(r\right)$. The generalized momenta corresponding to r and \theta are given:
a. $m{\dot{r}}^2,\ mr^2\dot{\theta}$
b. $m{\dot{r}}^2,\ mr^2{\dot{\theta}}^2$
c. $\mathbf{m\dot{r},\ mr^2\dot{\theta}}$
d. $Unpredictable$
199: Legendre transformation creates a new function :
a. With different transformation but same variable
b. With same transformation but different variables
c. No transformation
d. None
200: We apply Legendre transformation to the potential energy and transform it into:
a. Entropy
b. Pressure
c. Volume
d. Enthalpy
201: The dimensions of generalized momentum are:
a. Always those of angular momentum
b. Always those of linear momentum
c. Maybe those of angular momentum
d. None
202: Isotropy of space means that the system is invariant under:
a. Translation in time
b. Rotation in space
c. Translation in space
d. All of these
203: For a system of N-particles the dimension of phase space is:
a. 2N
b. 3N
c. $\mathbf{6N}$
d. 9N
204: The Hamiltonian can be constructed from the Lagrangian using the formula:
a. $H=\dot{p_i}\dot{q_i}-L$
b. $\mathbf{H=p_i\dot{q_i}-L}$
c. $H=\frac{\partial L}{\partial\dot{q_i}}$
d. $H=\frac{1}{L}$
205: Hamiltonian is a function of:
a. Variable energies
b. Conserved energies
c. Sum of energies
d. Different energies
206: Hamilton canonical equations of motion for a conservative system are:
a. $\dot{q_i}=-\frac{\partial H}{\partial\dot{p_i}}\ and\ \dot{p_i}=\frac{\partial H}{\partial\dot{q_i}}$
b. $\dot{q_i}=\frac{\partial H}{\partial\dot{q_i}}\ and\ \dot{p_i}=-\frac{\partial H}{\partial\dot{p_i}}$
c. $\dot{q_i}=-\frac{\partial H}{\partial\dot{q_i}}\ and\ \dot{p_i}=\frac{\partial H}{\partial\dot{p_i}}$
d. $\dot{\mathbf{q}\mathbf{i}}=\frac{\partial H}{\partial\dot{\mathbf{p}\mathbf{i}}}\ \mathbf{and}\ \dot{\mathbf{p}\mathbf{i}}=-\frac{\partial H}{\partial\dot{\mathbf{q}\mathbf{i}}}$
207: Law of conservation of linear momentum is a consequence of:
a. Homogeneity of time
b. Homogeneity of space
c. Isotropy of space
d. All of these
208: Law of conservation of energy is a consequence of:
a. Homogeneity of space
b. Isotropy of space
c. Homogeneity of time
d. a & b
209: Whenever the Lagrangian for a system does not contain a coordinate explicity:
a. $q_k$ is cyclic coordinate
b. $p_k$ is cyclic coordinate
c. $p_k$ , the generalized momentum is a constant of motion
d. a & c
210: Law of conservation of angular momentum is a consequence of:
a. Homogeneity of space
b. Homogeneity of time
c. Isotropy of space
d. a & b
211: If Lagrangian of a closed system is invariant under rotation then the ……… of a system is constant vector in time:
a. Linear momentum
b. Angular momentum
c. Force
d. Kinetic energy
212: The generalized momentum px of a particle of mass m with velocity ![]()
in an electromagnetic field is:
a. $p_x=mv_x$
b. $p_x=qv_xA_x$
c. $p_x=mv_x-qA_x$
d. $\mathbf{p_x=mv_x+qA_x}$
213: The angular momentum of coordinate ![]()
moving under central force is:
a. Zero
b. Variable
c. Negative
d. Constant
214: Position and momentum space in combined form is called:
a. Polar space
b. Cartesian space
c. Phase space
d. Hilbert space
215: Results of Lagrangian and Hamiltonian analysis are always:
a. Different
b. Same
c. Sometimes same sometimes different
d. None
216: The product of generalized momentum and associated coordinate have dimensions of:
a. Angular momentum
b. Linear momentum
c. Force
d. Energy
217: Choose the correct statement:
a. The angular momentum is conserved for a system possessing rotational symmetry
b. If Lagrangian of a system is invariant under translation along a direction the corresponding linear momentum is conserved
c. For a conservative system the Hamiltonian is equal to sum of kinetic energy and potential energy
d. All of these
218: In absence of a given component of applied force the corresponding component of linear momentum is:
a. Not conserved
b. Conserved
c. Equal to force
d. None
219: Whenever the Lagrangian function does not contain a coordinate ![]()
explicity , the generalized momentum is:
a. Holonomic
b. Derivative of motion
c. Integral of motion
d. None
220: If the Lagrangian is cyclic in ![]()
then:
a. $p_i$ is not conserved
b. $\mathbf{p}_\mathbf{i}$ is conserved
c. $q_i$ appears in Lagrangian
d. All of these
221: If A and B are any two constants of motion their Poisson bracket is:
a. Invariant
b. Zero
c. Constant of motion
d. Covariant
231: The transformation $\left(q,p\right)\rightarrow\left(Q,P\right)$ is canonical if:
a. $\left{q,P\right}=1$
b. $\left{Q,p\right}=1$
c. ${P,P}=1$
d. $\left{\mathbf{Q},\mathbf{P}\right}=\mathbf{1}$
232: The Poisson bracket of two dynamical variables f & g obeys:
a. $\left{\mathbf{f},\mathbf{g}\right}={\mathbf{g},\mathbf{f}}$
b. $\left{f,g\right}={g,g}$
c. $\left{f,g\right}=fg$
d. $\left{f,g\right}=-{g,f}$
233: A dynamical variable A$\left(q_i,p_i\right)$ is a constant of motion if its Poisson bracket commutes with:
a. Lagrangian
b. Hamiltonian
c. Angular momentum
d. Energy
234: If the Poisson bracket of a function with Hamiltonian vanishes then function is:
a. Constant of motion
b. Does not depend on time explicity
c. a & b
d. None
235: The correct relations for Poisson brackets are:
a. $\left[\ q_i,\ q_j\right]=\ \delta_{ij}$
b. $\left[\ q_i,\ p_j\right]=1$
c. $\left[\ q_i,\ q_j\right]=0$
d. b & c
236: For the Lagrange brackets which of the following is correct:
a. $\left{q_i,\ q_j\right}=\ \delta_{ij}$
b. $\left{\ q_i,\ p_j\right}=\ \delta_{ij}$
c. $\left{\ p_i,\ p_j\right}= 0$
d. b & c
237: Poisson brackets for angular momentum components $L_x,\ L_y,\ L_z$ satisfy the relation:
a. $\left[L_x,p_x\right]=0$
b. $\left[L_x,p_z\right]=-p_y$
c. $\left[L_y,L_z\right]=L_x$
d. All of these
238: If pi and qi (i=1,2,3) represent the momentum and position coordinates respectively for a particle:
a. The configuration space is three dimensional
b. The phase space is six dimensional
c. a & b
d. The configuration space is six dimensional
239: The phase space refers to:
a. Position coordinates
b. Momentum coordinates
c. Position and momentum coordinates
d. All of these
240: If we make a canonical transformation from set of variables $\left(P_i,\ Q_i\right)$ to new set of variables $\left(p_i,\ q_i\right)$ and the transformed Hamiltonian is identically zero then the:
a. New variables are constant in time
b. New variables are cyclic
c. Old variables remain constant in time
d. a & b
241: For a one dimensional harmonic oscillator the representative point in two dimensional phase space traces the:
a. Hyperbola
b. Parabola
c. Ellipse
d. Straight line
242: In case of canonical transformations:
a. Hamilton’s principle is satisfied in old as well as new variables
b. The form of Hamilton equations is preserved
c. a & b
d. None
243: If the generating function has form $F=\left(q_i,\ p_i,t\right)$ then:
a. $\mathbf{p_i=\frac{\partial F}{\partial q_i}\ and\ Q_i=\frac{\partial F}{\partial P_i}}$
b. $p_i=-\frac{\partial F}{\partial q_i}\ and\ Q_i=\frac{\partial F}{\partial P_i}$
c. $p_i=\frac{\partial F}{\partial q_i}\ and\ Q_i=-\frac{\partial F}{\partial P_i}$
d. $p_i=-\frac{\partial F}{\partial q_i}\ and\ Q_i=-\frac{\partial F}{\partial P_i}$
244: Choose the correct statement:
a. The generating function $F=\sum_{i}{q_iP_i}$ generates the identity transformation
b. The generating function $F=-\sum_{i}{q_iP_i}$ generates the identity transformation $p_i=-P_i and {Q_i=-q}_i$
c. The generating function $F=\sum_{i}{q_iP_i}$ cannot generate the identity transformation
d. a & b
245: Which one of the following is known as Newton’s law?
a. Law of inertia
b. Action ad reaction
c. Law of force
d. a & b
246: For a conservative force curl of must be equal to ____?
a. 1
b. Infinity
c. Zero
d. None
247: Laws of newton are not applicable to____?
a. Quantum mechanics
b. Classical mechanics
c. None
248: The strong form of newton’s law is valid if two forces have?
a. Same line of action
b. Different line of action
c. Same direction
d. a & c
249: Which one of the following assumption we made about the inertial space during the motion of free particle in it?
a. Homogenous
b. Isotropic
c. Heterogeneous
d. a & b
250: The mass determining the acceleration of a body under the action of force is called ____?
a. Inertial mass
b. Accelerated mass
c. Gravitational mass
251: ____ are the factors that restrict the motion of a body?
a. Constraints
b. Forces
c. Friction
d. None
252: Scleronomic and rheonomic are the types of _____ constraint?
a. Non-holonomic
b. Holonomic
c. a & b
d. None
253: Holonomic constraints are also known as?
a. Differentiable constraints
b. Integrable constraints
c. Partially integrable constraints
d. Non-integrable constraints
254: Gas molecules in a container, particles moving in a sphere are the examples of?
a. Holonomic constraint
b. Non-Holonomic constraint
c. Scleronomic constraint
d. Rheonomic constraint
255: The constraints which contain time explicity are called _____?
a. Holonomic constraint
b. Non-Holonomic constraint
c. Scleronomic constraint
d. Rheonomic constraint
256: A scleronomic constraint is independent of time.
a. True
b. False
257: Configuration space is ____ dimensional space?
a. 1
b. 3
c. n
d. Infinite
258: Which one of the following is the property of virtual displacement?
a. Infinitesimal
b. Occur at given instant of time
c. Consistent with constraints
d. All
258: For what type of equilibrium Principle of Virtual Work is applicable?
a. Static equilibrium
b. Dynamic equilibrium
c. Both
d. None
259: D’ Alembert Principle is suggested by ____ and developed by ____?
a. D’Alembert, D’Alembert
b. D’ Alembert , Bernoulli
c. Bernoulli , D’ Alembert
d. Bernoulli, Bernoulli
260: What is the angle between constraints and virtual displacement?
a. 0
b. 90
c. 45
d. 180
261: Which law of newton is used in D’ Alembert principle?
a. 1st
b. 2nd
c. 3rd
d. None
262: For what type of equilibrium is D’ Alembert principle applicable?
a. Static equilibrium
b. Dynamic equilibrium
c. Both
d. None
263: Sum of internal forces is equal to ____?
a. 0
b. 1
c. F
d. None
264: The Lagrange from Lagrangian equation is equal to?
a. T = L –V
b. L= T- V
c. L= V – T
d. L = T –Q
265: What is the degree of freedom of Atwood machine?
a. One
b. Two
c. Three
d. Four
267: What is the kinetic energy of simple pendulum?
a. $\mathbf{12m}\mathbf{l}^\mathbf{2}\mathbf{\theta}^\mathbf{2}$
b. $12mv^2$
c. $12mx^2$
d. None
268: Which principle is used to find the trajectory of path at any instant of time?
a. Lagrange
b. Hamilton
c. D’ Alembert
d. None
269: Hamilton’s principle is also known as ___?
a. Variational principle
b. Principle of least action
c. Action integral
d. a & b
270: Path of projectile is parabola is an example of?
a. Lagrange
b. Hamilton
c. D’ Alembert
d. None
272: What is the equation of parabola?
a. $\mathbf{y}=\mathbf{a}\mathbf{x}^\mathbf{2}+\mathbf{bx}$
b. $x =-ax^2+bx$
c. $x=-ay^2+by$
d. None
273: Which one of the following is a central force?
a. Gravitational force
b. Coulomb force
c. Magnetic force
d. a & b
274: What is the property of central force motion?
a. P=0
b. L=0
c. F=0
275: For a central force the magnitude depends only on distance from center.
a. True
b. False
276: In central motion direction of angular momentum is always _____ to plane?
a. Tangent
b. Perpendicular
c. Normal
277: The system in which one of the particle is moving while other is at rest is called _______?
a. Mass coordinate system
b. Laboratory coordinate system
c. Acceleration coordinate system
d. None
278: The direction of motion of incident particle is center of mass is _____ as the direction of motion of incident particle in laboratory frame.
a. Same
b. Different
c. Opposite
d. None
279: At which angle in laboratory coordinate system, the two particles move off to one another after collision?
a. Normal
b. Tangent
c. Right angle
d. None
280: Impact parameter is the perpendicular distance between center of force and incident velocity.
a. True
b. False
281: From which particle of atomic nuclei Rutherford scattering formula is derived?
a. Alpha
b. Beta
c. Gamma
282: The set of 2n equation is known as ______?
a. Hamilton equation
b. Canonical equation
c. Equation of motion
d. All of above
283: A coordinate that do not appear explicitly in the Lagrangian of a system is said to be _____?
a. Cyclic coordinate
b. Ignorable coordinate
c. a & b
d. None
284: The generalized momentum conjugate to a cyclic coordinate remains _____ during a motion
a. Constant
b. Conserved
c. Non-conserved
d. None
285: Homogeneity of time leads to the conservation of ______?
a. Linear momentum
b. Energy
c. Angular momentum
d. All
286: Homogeneity of space leads to the conservation of ______?
a. Energy
b. Linear momentum
c. Angular momentum
d. All
287: Isotropy of space leads to the conservation of ______?
a. Energy
b. Linear momentum
c. Angular momentum
d. All
288: For which quantity Hamiltonian is constant?
a. t
b. p
c. L
d. V
289: Which one of the following equation is true about Hamiltonian?
a. H=E
b. H=p
c. H=Q
d. H=L
290: Inverse of canonical transformation is_____?
a. Identity
b. Canonical
c. Non-canonical
d. Conserved
291: Which system constitute Poisson bracket?
a. Holonomic constraint
b. Non-Holonomic constraint
c. Scleronomic constraint
d. Rheonomic constraint
292: The concept of Poisson bracket was introduced by?
a. F.D. Poisson
b. S.D. Poisson
c. G.C. Poisson
d. None
293: Poisson first theorem states that ____?
a. $\left[\mathbf{u},\mathbf{H}\right]=\mathbf{0}$
b. $\left[u,P\right]=0$
c. $\left[H,P\right]=0$
d. All of these
294: The equation $\left[F,G\right]=constant$ belongs to?
a. Poisson first theorem
b. Poisson second theorem
c. Poisson third theorem
d. All of these
295: The canonical equations of motion are ______ in the property of Poisson bracket?
a. Constant
b. Implicit
c. Explicit
d. Conserved
296: Which one of the following is the type of canonical transformation?
a. Point transformation
b. Coordinate transformation
c. a & b
d. None
297: According to the principle of least action:
a. $\int{\left(\sum_{k}{p_k\dot{q_k}}-H\right)dt=0}$
b. $\int{\sum_{k}{p_k\dot{q_k}}dt=0}$
c. $\int{(H+L)dt=0}$
d. b & c
298: The modified Hamilton’s principle is given by:
a. $\mathbf{\delta\sum_{j}{\int_{t_1}^{t_2}{p_jdq_j-\delta}\int_{t_1}^{t_2}Hdt=0}}$
b. $ \delta\sum_{j}{\int_{t_1}^{t_2}{p_jdq_j+\delta}\int_{t_1}^{t_2}Hdt=0}$
c. $\delta\sum_{j}{\int_{t_1}^{t_2}{p_jdq_j-\delta}\int_{t_1}^{t_2}{Hdq_j}=0} $
d. $\delta\sum_{j}{\int_{t_1}^{t_2}{p_jdq_j-\delta}\int_{t_1}^{t_2}{Hdq_j}=0}$
299: Hamilton’s principle function S and Hamilton’s characteristic function W for conservative system are related as:
a. S=W
b. $\mathbf{S}=\mathbf{W}-\mathbf{Et}$
c. S=W+Et
d. S is not related to
300: The action and angle variables have dimensions of:
a. Force and angle
b. Energy and angle
c. Angular momentum and angle
d. Dimensionless quantities
