Mechanics-I - Quanta: BS/MSc Physics Books

Note: The Correct Answer of each MCQ has been bolded.

1. A vector is represented graphically by a directed line according to suitable scale with:

a. Temperature

b. Time

c. An-arrow-head

d. All of above

2. The direction of a vector in space is specifiaed by the:

a. One angle

b. Two angles

c. Three angles

d. All of above

3. If a vector makes an angle with x-axis, then its x-component is:

a. A

b. Acosθ

c. Asinθ

d. All of above

4. If position two aeroplanes at any instant in given by (2, 3,4) and (5,6,7) from origin in kilometres, then distance between position of two aero planes will be:

a. 4.8km

b. 5km

c. 5.2 km

d. zero

5. If resultant vector lies in 2^nd quadrant, then its direction is;

a. θ=φ

b. θ=180^o+φ

c. θ=180^o-φ

d. θ=270^o-φ

6. Two forces act together on an object, then magnitude of their resultant is maximum when angle between forces is:

a. θ=0^o

b. θ=180^o

c. θ=270^o

d. θ=45^o

7. The resultant of magnitude of two forces 6N and 8N acting at right angle to each other is:

a. 14 N

b. 2N

c. 10 N

d. 8 N

8. The magnitude of resultant of two forces acting at right angle to each other is:

a. $F_1^2+F_2^2$

b. $\mathbf{\sqrt{F_1^2+F_2^2\ }}$

c. $\sqrt{F_1+F_2}$

d. Zero

9. When two forces of equal magnitude make an angle of with each other, then magnitude of their resultant is:

a. 10 N

b. Maximum

c. Zero

d. 8 N

10. If resultant of two vectors each of same magnitude is also of same magnitude, then angle between them is:

a. 30^o

b. 45^o

c. 90^o

d. 120^o

11. The example of vector product is:

a. Torque

b. Angular momentum

c. Linear velocity

d. All of above

12. The vector product of anti-parallel vectors is:

a. Zero

b. Maximum

c. One

d. All of these

13. Vector product of with itself is:

a. A²

b. Asinθ

c. A

d. Zero

14. The magnitude of is equal to area of ____________ with as its adjacent sides:

a. Square

b. Triangle

c. Hexagon

d. None of the above

15. Half of magnitude of is equal to area of _____________ with as its adjacent sides:

a. Square

b. Triangle

c. Hexagon

d. None of the above

16. If points along x-axis, then must lie in:

a. -plane

b. -plane

c. -plane

d. All of above

17. A particles starts from center O towards OA, then moves along AB and stops at B. If the displacement of particle is:

a. $100\sqrt2\ m$

b. $\left(\frac{100}{\sqrt2}\right)m$

c. 100 m

d. None of the above

18. Mark the wrong statement:

a. $\hat{i}.\left(\hat{j}\times\hat{K}\right)=\hat{i}.\hat{j}\times\hat{k}$

b. $\hat{\mathbf{A}}\times\left(\hat{\mathbf{B}}\times\hat{\mathbf{C}}\right)=\left(\hat{\mathbf{A}}\ \times\ \hat{\mathbf{B}}\right)\times\hat{\mathbf{C}}$

c. $\left(\hat{i}.\hat{j}\right)^2+\left(\hat{j}.\hat{j}\right)^2+\left(\hat{k}.\hat{k}\right)^2$

d. $\vec{A}.\hat{i}=A_x$

19. The position vector of a particle moving along a curve in cylindrical polar coordinates is:

a. $\vec{\mathbf{r}}\left(\mathbf{t}\right)=\mathbf{\rho}\hat{\mathbf{\rho}}+\ \mathbf{z}\hat{\mathbf{k}}$

b. $\vec{r}\left(t\right)=\hat{\rho}+\ z\hat{k}$

c. $\vec{r}\left(t\right)=\rho\hat{\rho}$

d. None of the above

20. Three coplanar forces acting on a body keep it in equilibrium. This should therefore be:

a. Concurrent

b. Non-concurrent

c. Parallel

d. All of the above

21. A unit vector in terms of direction cosines can be written as:

a. $\hat{\mathbf{A}}=\mathbf{cos\alpha}\ \hat{\mathbf{i}}+\mathbf{cos\beta}\ \hat{\mathbf{j}}+\ \mathbf{cos}\ \hat{\mathbf{k}}$

b. $\hat{A}=x\hat{i}+y\hat{j}+z\hat{k}$

c. $\hat{A}=cos\alpha\ \hat{i}+cos\beta\ \hat{j}$

d. All of the above

22. Three unit vectors are:

a. Concurrent

b. Perpendicular

c. Parallel

d. All of the above

23. The direction of is always:

a. Perpendicular to surface φ= constant

b. Parallel to surface φ=constant

c. Perpendicular or Parallel to surface φ=constant according to geometry of problem

d. None of the above

24. Derivative of velocity with respect to time is called:

a. Displacement

b. Momentum

c. Acceleration

d. None of the above

25. The vector field is solenoidal if:

a. $\mathbf{div}\ \vec{\mathbf{A}}=\mathbf{0}$

b. $curl\vec{A}=0$

c. $curl\vec{A}\neq0$

d. None of the above

26. If $\vec{A}.\frac{d\vec{A}}{dt}=0$ then vector $\vec{A}$ has :

a. Constant magnitude

b. Variable magnitude

c. a & b

d. None of the above

27. If vector field can be expressed as gradient of a scalar ф, then vector field is known as:

a. Solenoidal

b. Irrotational

c. Conservative

d. None of Above

28. The divergence of position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ is:

a. Zero

b. 3

c. 1/2 + 3

d. None of the above

29. The curl of position vector $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$ is:

a. Zero

b. 3

c. 1/2 + 3

d. None of the above

30. The divergence of curl of a vector is always equal to:

a. Zero

b. 3

c. 1/2 + 3

d. None of the above

31. The curl of gradient of a scalar is always equal to:

a. Zero

b. 3

c. 1/2 + 3

d. None of the above

32. The linear integral of a vector field is equal to:

a. $\int_{\mathbf{s}}^{\ }{\mathbf{curl}\ \vec{\mathbf{A}}.\vec{\mathbf{ds}}}$

b. $\oint{curl\vec{A}}.\vec{dr}$

c. $\int_{s}^{\ }{\vec{A}.\vec{ds}}$

d. None of the above

33. The volume integral of divergence of a vector field is equal to:

a. $\int_{s}^{\ }{curl\ \vec{A}.\vec{ds}}$

b. $\oint{curl\vec{A}}.\vec{dr}$

c. $\int_{\mathbf{s}}^{\ }{\vec{\mathbf{A}}.\vec{\mathbf{ds}}}$

d. None of the above

34. For a conservative field :

a. $\int_{s}^{\ }{curl\ \vec{A}.\vec{ds}}$

b. $\oint\vec{\mathbf{A}}.\vec{\mathbf{dr}}=\mathbf{0}$

c. $\int_{s}^{\ }{\vec{A}.\vec{ds}}$

d. All of above

35.If a vector makes an angle with x-axis, then its y-component is:

a. A

b. Acosθ

c. Asinθ

d. Zero

36. If are perpendicular to each other, then:

a. $\vec{A}=\vec{B}$

b. $\left|\vec{\mathbf{A}}\right|=\left|\vec{\mathbf{B}}\right|$

c. $\left|\vec{A}\right|\neq\left|\vec{B}\right|$

d. All of the above

37. Example of scalar product is:

a. Torque

b. Angular momentum

c. Work

d. All of above

38. Two vectors and are making an angle with each other , then scalar projection of on is:

a. $\frac{\vec{\mathbf{A}}.\vec{\mathbf{B}}}{\left|\vec{\mathbf{A}}\right|}$

b. $\frac{\vec{A}.\vec{B}}{\left|\vec{B}\right|}$

c. $\left|\vec{A}\right|cos\theta$

d. All of above

39. The rain is vertically with a speed 4m/s and the man is moving due east with speed 3m/s. With what speed, the rain appears to be coming to man?

a. 5m/s

b. 1m/s

c. 7m/s

d. None of the above

40. The direction of vector product can be found by_______ rule:

a. Right hand

b. left hand

c. Fleming

d. None of above

41. If $\vec{A}.\vec{B}=0$ , then value of $\vec{A}\times\vec{B}$ will be:

a $AB\hat{n}$

b. Zero

c. One

d. None of above

42. Which of the following group represents vector only;

(a) acceleration, force, mass (b) perpendicular to each other

43. If $\vec{A}\times\vec{B}=0\ \ \vec{A}.\vec{B}=0,$ then A & B are:

a. Parallel to each other

b. Perpendicular to each other

c. Both are null vector

d. All of the above

44. $\vec{A}\times\vec{B}$ for two non zero parallel vectors is :

a. $AB\ sin\theta\ \hat{n}$

b. One

c. $AB\ cos\theta\ \hat{n}$

d. None of above

45. A fluid that has non-vanishing curl is called:

a. Vortex field

b. Conservative field

c. Fleming field

d. None of above

46.Electric field is an example of;

a. Vector field

b. Scalar field

c. Right field

d. None of above

47. Grads has direction in which S changes most rapidly and its magnitude is _________ derivative of S :

a. Directional

b. Partial

c. Ordinary

d. All of above

48. Scalar product of differential operator ∇ with itself is called:

a. Dell operator

b. Laplacian operator

c. Momentum operator

d. All of above

49. Relation between surface and line integrals is given by;

a. Stoke’s Theorem

b. Divergence theorem

c. Coulomb theorem

d. None of above

50. A particle moves along the circular path with constant speed. What is nature of its acceleration?

a. Its magnitude changes

b. Its direction changes

c. It is uniform

d. zero

51. A simple pendulum hangs from ceiling of a train. The string is included towards the rear of the train What is nature of motion of train:

a. Retarded

b. Uniform

c. Accelerated

d. At rest

52. A particle moves in a plane with acceleration having direction different than that of the instantaneous velocity. What is nature of trajectory:

a. Ellipse

b. Hyperbola

c. Parabola

d. Straight line

53. A particle travels according to the equation, x=acosωt & y=bcos(ωt + 45^o) The trajectory is,

a. Rectangular Hyperbola

b. Cycloid

c. Oblique ellipse

d. zero

54. A passenger travelling in a train moving with constant velocity drops a stone from window. To the passenger the path of stone will be;

a. Arc of circle

b. Elliptical

c. Straight line

d. None of above

55. The time Elapsed is plotted along x-axis and acceleration is plotted along y-axis. The area between graph and x-axis is gives:

a. Difference in acceleration

b. Average velocity

c. Difference in velocities

d. Distance covered

56. The angular speed of minute hand of clock in degrees per second is:

a. 1.0

b. 0.1

c. 0.001

d. None of the above

57. The angular acceleration of a particle moving along a circle with uniform speed is:

a. Uniform but not zero

b. Zero

c. Incomplete information

d. Variable

58. A stone of mass m tied to a string of length ‘l’ is rotated in a circle with the other end of string as the center. The speed of stone is ‘v’. If sting breaks, the stone will move:

a. Along a tangent

b. Toward center

c. Away from center

d. None of above

59. A bottle of soda water is held by the neck and swing briskly in a horizontal circle. Near which position of the bottle do the bubbles collect:

a. In the middle of bottle

b. Near bottom

c. Near the neck

d. Bubbles uniform distributed

60. A car is taking a turn on a level road. It may be thrown towards because of the:

a. Reaction of ground

b. Frictional force

c. Weight

d. Lack of centripetal force

61. An automobile is turning a circular road radius ‘r’. The coefficient of friction between the tyres and road is ‘µ ’. The velocity of vehicle should not be more than

a. $\sqrt{\frac{\mu\ g}{r}}$

b. $\sqrt{\mathbf{\mu}\ \mathbf{g}\ \mathbf{r}}$

c. $\mu\ g\ r$

d. $\frac{\mu\ g}{r}$

62. A particle moves according to equation , retardation at any instant is:

a. $\mathbf{\frac{2a}{{\ \left(2ax+b\right)}^3}}$

b. 2a

c. $\frac{2a}{\left(2ax+b\right)^2}$

d). Zero

63. A bus is standing at bus stop. A man is in front of bus stop. Suddenly the bus starts moving with an acceleration 2m/s². The man notices the bus moving after 2s of its motion. With what constant speed man should run so as to get in the bus in 2s when he notices the bus moving:

a. 8 m/s

b. 2m/s

c. 4m/s

d. 6m/s

64. The displacement of particle moving in one direction is, x is in meters and t is in seconds. The displacement when velocity is zero:

a. 3m

b. 1m

c. 1.8m

d. None of the these

65. Which of the following can be zero when a particle is in motion for some time?

a. Speed

b. displacement

c. Time

d. All of above

66. The velocity time graph of motion stating from rest with uniform acceleration is a straight line:

a. Not passing through origin

b. Parallel to time axis

c. Parallel to velocity axis

d. None of the above

67. If a distance covered by a particle is zero, then what we can say about its displacement:

a. It is negative

b. It must be zero

c. It may or may not be zero

d. It cannot be zero

68. A bucket is placed in the open where the rain is falling vertically. If wind begins to blow at double the velocity of rain, how will the rate of filling of bucket change :

a. Half

b. Double

c. Quadrupole

d. remains constant

69. The displacement of particle is given by, $\sqrt x=\sqrt t+1$ Which of the following statement about velocity is true?

a. Increases with time

b. Decreases with time

c. Zero

d. Constant but not zero

70.The slop of velocity time graph for uniform motion is:

a. Zero

b. Infinite

c. Positive

d. Negative

71. An object is launched into air with an initial velocity ${\vec{v}}_0=4\hat{i}+5\hat{j}$ Ignore air resistance. At highest point, magnitude of velocity is:

a. $\sqrt{4^2+5^2}$

b. $\sqrt{\mathbf{4}^\mathbf{2}}$

c. $\sqrt{5^2}$

d. Zero

72. Suppose net force on an object is zero, which of the following could be constant:

a. Speed

b. Position

c. Acceleration

d. Velocity

73. Rain drops fall with constant velocity. This suggests:

a. Gravitational field does not act on drop

b. Force acting on rain drop is zero

c. The size of rain drop is so small that acceleration does not build up

d. Due to viscosity

74. Rain is falling vertically downwards. To a man running eastward, the rain will be appear to coming from:

a. East

b. West

c. Northeast

d. None of the above

75. A moving body is covering the distance directly proportional to the cube of time. The acceleration of body is:

a. Constant

b. Increasing

c. Zero

d. Decreasing

76. A stone is thrown upward which rises to a height of 100m. The relative velocity of stone with respect to earth will be maximum at:

a. Height of 50m

b. The highest point

c. The ground

d). None of Above

77. A ball is thrown horizontally from top of tower. What happens to horizontal component of velocity?

a. First increases and then decreases

b. Remains same

c. Increases

d. Decreases

78. A projectile is thrown at an angle of with horizontal and its range is . Another projectile is thrown at an angle of with vertical and its range is . The relation between is:

a. R₂=2R₁

b. R₁=2R₂

c. R₁=R₂

d. None of the above

79. An object is projected upwards. Its acceleration at highest point is:

a. Zero

b. Downwards

c. Cannot be predicted

d. Upwards

80. If a man wants to hit a target, he should aim his rifle in a direction:

a. Lower than the target

b. Of the target

c. Higher than the target

d. None of the above

81. A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of mud are thrown:

a. Vertically inward

b. Vertically upward

c. Horizontally to south

d. Horizontally to north

82. A block of metal is lying on the floor of bus. Maximum acceleration which can be given to the bus so that the block remain may at rest, will be:

a. µg²

b. µ²g

c. µg

d. None of the above

83. A body moving in a circular motion with constant speed has:

a. Kinetic energy changes by

b. Momentum does not change

c. Momentum change by

d. Kinetic energy changes by

84. A body moving in a circular motion with constant speed has:

a. Constant Kinetic energy

b. Constant acceleration

c. Constant velocity

d. Constant displacement

85. Two racing cars of masses are in circles of radii respectively. Their speeds are such that each makes a complete circle in the same length of time t. The ratio of angular speed of the 1^st and 2^nd car is:

a. m₁:m₂

b. r₁:r₂

c. 1:1

d. m₁r₁:m₂r₂

86. If the earth were to rotate faster than its present speed, the weight of an object will:

a. Increase at the equator but remains unchanged at poles

b. Decrease at the equator but remains unchanged at poles

c. Remains unchanged at the equator but increases at poles

d. Remains unchanged at the equator but decreases at poles

87. A pendulum is clapped on the roof a stationary car and its time period is T. If car starts to move with acceleration a then its time period will be:

a. More than T

b. Infinite

c. Equal to T

d. Less than T

88. Which of the following can be zero when the particle is in motion for some time?

a. Speed

b. Velocity

c. Distance

d. None of the above

89. A particle moves according to law, $\mathbf{{\color{DarkBlue} }t=\ \sqrt x+2}$ t is in second and is in meters, then acceleration of particle is:

a. Constant but not uniform

b. Non- uniform

c. Uniform

d. None of above

90. A particle moves in straight line so that its displacement in meters at time t is such that, $\mathbf{t=\sqrt{x^2-1}}$ Its acceleration in m/ is:

a. $\frac{1}{x^3}$

b. $\frac{1}{x}$

c. $\frac{-t}{x^2}$

d. none of above

91. An iron ball and a wooden ball of same radius are released from a height to a vacuum. The time taken by both of them to reach ground is;

a. Unequal

b. Exactly equal

c. Roughly equal

d. Zero

92. Two bullets are fired horizontally with different velocities from same height. Which will reach first:

a. Slower one

b. Cannot be said

c. Faster one

d. Both will reach simultaneously

93. A ball is projected upward. Its velocity at highest point is:

a. Downward

b. Upward

c. Zero

d. Horizontal

94. Two boats are moving in same direction in a river. What is best condition so that they move parallel in same direction?

a. Both move away from each other

b. They are slightly bent towards each other

c. They are parallel to each other

d. It is not possible

95. When we walk on ice, we should take small steps to avoid slipping. This is because smaller steps ensure:

a. Large friction

b. Smaller friction

c. Larger normal force

d. Smaller normal force

96. If a rough surface is polished beyond a certain limit then magnitude of frictional force will:

a. Increase

b. Decrease

c. Non-uniform

d. None of above

97. Two spheres of equal masses but radii r and 2r are allowed to fall in a liquid; the ratio of their terminal velocities:

a. 1:4

b. 2:1

c. 1:32

d. None of above.

98. A body is dropped from a tower with zero velocity, reaches ground in 4s. The height of tower is;

a. 80m

b. 20m

c. 160m

d. Zero

99. A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterized by:

a. Negative slop and zero curvature

b. Zero-Slop and negative curvature

c. Zero slop and positive curvature

d. Cannot be said

100. A cold soft drink is kept on balance. When the cap is opened, then weight ;

a. Increases

b. Decreases

c. Remains same

d. First increases and then increases

Class: Subject: Mechanics

Chapter # 3: Work, Power and Energy Category: Multiple Choices (MCQ’s)

101. A body is acted upon by force which varies inversely as distance x covered. The work done body is proportional to:

a. x²

b. x

c. x^1/2

d. All of above

102. The kinetic energy of a body varies directly as time t elapsed. The force varies directly as:

a. $\frac{\mathbf{1}}{\sqrt\mathbf{t}}$

b. $\sqrt t$

c. t

d. All of above

103. The displacement x and time t for a particle are related to each other as, $t=\sqrt x+3$ What is work done in 1^st six seconds if its motion if mass is 2kg?

a. Zero

b. 2 J

c. 6J

d. None of above

104. A ball with initial kinetic energy K is projected at an angle of from horizontal. Its kinetic energy at highest point of motion will be:

a. K

b. K/2

c. 3K/2

d. None of above

105. Two workers X and Y are loading identical cement blocks onto Y’s tractor trolley. X lifts his block straight up from the ground to the trolley, whereas Y slides his block up a ramp containing frictionless rollers. Which statement is true about the work done on the block-Earth system?

a. X does more work than Y

b. X and Y do the same amount of work

c. Y does more work than X

d. None of above

106. A particles moves under the influence of a force from 0 to . The work done in this process will be:

a. $\frac{Kx^2}{2}$

b. kx³

c. Zero

d. kx²

107. In the tug of war A is slowly being defeated by team B. Network is being done by:

a. Team A

b. Team B

c. Both

d. None of the above

108. A spring of spring constant k is given a sharp blow by a force F so that the spring shows a compression x. The work done on spring is:

a. $\frac{1}{\ 2}kx^2$

b. kx³

c. $\frac{1}{4}{kx}^2$

d. None of above

109. You hold a slingshot at arm’s length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 2m/s. With the same procedure, you fire a bean with speed 6m/s. What is the ratio of the mass of the bean to the mass of the pebble?

a. 1/9

b. 9

c. 3

d. 1/3

110. The angles between force and displacement for maximum and minimum work will be respectively:

a. 0^o & 180^o

b. 180^o & 0^o

c. 90° & 0°

d. 0° & 90°

111. A block of mass m is taken to a height R_e/2. The work done is:

a. $\ \frac{1}{4}\ mgR_e$

b. $\frac{1}{2}\ mgR_e$

c. $\ \frac{\mathbf{1}}{\mathbf{3}}\ \mathbf{mg}\mathbf{R}_\mathbf{e}$

d. None of above

112. A cubical vessel of height 1m is full of water. The work done in taking water out of the vessel be:

a. Zero

b. 5J

c. Cannot be predicted

d. 5000J

113. The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of constant force is directly proportional to:

a. $\sqrt3$

b. m

c. Independent of m

d. None of above

114. Where will it be a profitable to purchase 1kg sugar?

a. At poles

b. At equator

c. At latitude

d. Cannot be predicted

115. Two electrons are brought closer together, the potential energy of system will:

a. Decrease

b. Increase

c. Zero

d. None of above

116. Sand is being dropped on a conveyer bell at rate of 2m kg per second. The force necessary to keep the belt at velocity of 2v m/s will be:

a. mv N

b. 4mv N

c. 2mv N

d. None of above

117. The potential energy of a system in a state of unstable equilibrium is:

a. Zero

b. Minimum

c. Maximum

d. None of above

118. The increase in potential energy of a body of mass m, when it is carried away from surface of earth to height equal to the radius of earth will be:

a. $2mgR_e$

b. $mgR_e$

c. $\frac{\mathbf{1}}{\mathbf{2}}\mathbf{mg}\mathbf{R}_\mathbf{e}$

d. None of above

119. A missile is released with a velocity less than the escape velocity. The sum of its potential and kinetic energies is:

a. Positive

b. Zero

c. mgh

d. Negative

120. A pile driver drives posts into the ground by repeatedly dropping a heavy object on them. Assume an object is dropped from the same height each time. By what factor does the energy of the pile driver ____________ Earth system change than the mass of the object being dropped is doubled?

a. half

b. 2

c. 4

d. The energy is same

121. The mechanical gain in a machine to overcome a resistance W by an effort P will be:

a. W-P

b. W×P

c. W/P

d. None of above

122. A bird weighs 2kg and is inside a cage of 1 kg. If it starts flying, then what is weight of bird and cage assembly?

a. 2kg

b. 4kg

c. 3kg

d. Zero

123. A fighter aircraft is moving in a vertical circle of radius r. Minimum velocity at highest point is:

a. $\sqrt{\mathbf{gr}}$

b. $\sqrt{\frac{gr}{2}}$

c. $\sqrt{3gr}$

d. $\sqrt{2gr}$

124. Given that v is speed, r is radius and g is acceleration due to gravity. Which of the following is dimensionless?

a. $\frac{\mathbf{v}^\mathbf{2}}{\mathbf{gr}}$

b. $\frac{v^2r}{g}$

c. $\frac{v^2g}{r}$

d. None of above

125. An ice cube has been given a push and slides without friction on a level table then it is:

a. in stable equilibrium

b. In unstable equilibrium

c. in neutral equilibrium

d. Not in equilibrium

126. A body of mass m is moved to a height h equal to radius of earth. The increase in potential energy is:

a. Zero

b. $\frac{\mathbf{1}}{\mathbf{2}}\ \mathbf{mg}\mathbf{R}_\mathbf{e}$

c. $mgR_e$

d. Cannot be predicted

127. In an elevator moving vertically up with an acceleration g, the force exerted on floor by a passenger of mass m is:

a. mg

b. 1/2 mg

c. independent of m

d. 2mg

128. Water is falling on blades of a turbine at a rate of 100 kg/s from a certain spring. If the height of spring be 100 m, the power transferred to turbine will be:

a. 1000kW

b. 10kW

c. 100W

d. Cannot be predicted

129. A certain spring that obeys Hook’s law is stretched by an external agent. The work done in stretching the spring by 0.1m is 4J. How much additional work is required to stretch the spring by an additional 0.1m? :

a. 2J

b. 4J

c. 12 J

d. 16 J

130. A ball of clay falls freely to the hard floor. It does not bounce noticeably, and it very quickly comes to rest. What, then, has happened to the energy the ball had while it was falling? :

a. It has been used up in producing the downward motion

b. It is in the ball and floor (and walls) as energy of invisible molecular motion

c. It has been transformed back into potential energy

d. Cannot be answered

131. The expression [ML²T^-2 ] represents:

a. Speed

b. Kinetic energy

c. Power

d. None of the above

132. A Force F is given by F= at + bt², where t is time. The dimension of a and b are:

a. [MLT^-3 ] & [ML²T⁴ ]

b. [ MLT^-3] & [ MLT^-4]

c. [MLT^-1 ] &[MLT⁰ ]

d. None of above

133. A bullet is fired from a rifle. If rifle recoils freely, then kinetic energy of rifle is:

a. Greater than that of bullet

b. Equal to that of bullet

c. Less than that of bullet

d. None of the above

134. The work done in taking a particle from floor to table depends on:

a. Actual path taken

b. Time taken in this work

c. Speed of particle

d. Height of table

135.A spring of spring constant k is cut into two pieces such that longer is twice the shorter. The spring constant of smaller one is:

a. k

b. 3k/2

c. 3k

d. Cannot be said

136. If the network done by external force on a particle is zero, which of the following statements about the particle must be true?:

a. Its speed is unchanged

b. Its velocity is decreased

c. Its velocity is unchanged

d. Its velocity is zero

137. A block of mass m is dropped from the fourth floor of an office building and hits the sidewalk below at speed v. From what floor should be block be dropped to double that impact speed?

a. 6^th floor

b. 8^th floor

c. 12^th floor

d. 16^th floor

138. Three identical masses of m are placed at the vertices of an equilateral triangle of side the work done to bring these masses to the vertices of an equilateral triangle of side is:

a. $\frac{Gm^2}{3l}$

b. $\frac{Gm^2}{2l}$

c. Zero

d. $\frac{\mathbf{3G}\mathbf{m}^\mathbf{2}}{\mathbf{2l}}$

139.If a particle covers half the circle of radius R with constant speed, then:

a. Momentum change is

b. Change in kinetic energy is

c. Change in kinetic energy is

d. Change in kinetic energy is zero

140. A truck of mass 10 ton is moving up an incline which rises 1 to 10. The coefficient of friction is 0.2. if velocity of truck is 10m/s , then power of engine if efficiency is 80% is:

a. $3\times{10}^5\ W$

b. $\mathbf{3}.\mathbf{75}\times{\mathbf{10}}^\mathbf{5}\ \mathbf{W}$

c. $3.\times{10}^6\ W$

d. None of above

141.A circular disc is rotating with angular velocity . A man sitting at edge walks towards the center of disc, then angular velocity:

a. Decreases

b. Increases

c. No change

d. None of above

142. When a simple pendulum swings back and forth, the forces, which of these forces, if any, does no work on the pendulum at any time?

a. Gravitational force

b. Tension in the supporting cord

c. Air resistance

d. Cannot be answered

143. Work done in increasing the length of wire 1m of cross section area by 1mm will be:

a) 0.1J (b) 1 J (c)1000 J (d) Cannot be said

144. A body of weight mg is hanging on string which extends its length by . The work done in extending the string is:

a. mgl

b. mgl/2

c. mgl2

d. 100 J

145.Surface area of a soap bulb is 1.3 with surface tension 1.3 . The work done to double the surface area will be:

a. 3.9 X 10^-7J

b. 3 X 10^-7J

c. 2.9 X 10^-4J

d. Cannot be said

146. The decrease in potential energy of a ball of mass 20 kg which falls from a height 50cm is:

a. 900J

b. 1980J

c. Zero

d. 98 J

147. The average resisting force that must act on a 5kg mass to reduce its speed from 65cm/s to 15cm/s in 0.2s is:

a. 12.5N

b. 25N

c. 50N

d. 100N

148. When a simple pendulum swings back and forth, the forces, which of these forces, if any, does negative work on the pendulum at all times during its motion?

a. Gravitational force

b. Tension in the supporting cord

c. Air resistance

d. Cannot be answered

149. What work is required to be done by external force on an object on frictionless, horizontal surface to accelerate it from a speed v to a speed 2v?

a. Twice the work required to accelerate the object from 0 to v

b. Three times the work required to accelerate the object from 0 to v

c. Four times the work required to accelerate the object from 0 to v

d. Not known without knowledge of the acceleration

150. If the speed of a particle is doubled, its kinetic energy becomes:

a. Four times larger

b. Two times larger

c. Half as large

d. Unchanged

151. The magnitude of the force of gravity between two identical objects is given by . If the mass of each object is doubled but the distance between them is halved, then the new force of gravity between the object will be:

a. 16F_o

b. 4F_o

c. 4F_o

d. F_o/2

152. The semi major axis of the orbits of mercury and mass in the astronomical units are 0.387 and 1.524 respectively. If the time period of mercury is 0.241 years, then time period of mars will be:

a. 2.9 years

b. 1.9 years

c. 0.19 years

d. All of above

153. A clock P is passed on pendulum motion and a watch S is based on spring motion. Both are made isochronous on earth. On a planet with density equal to that of earth but radius half that of earth?

a. S will run faster than P

b. P will run faster than S

c. Both will run with equal speed

d. None of above

154. The ratio of gravitational mass to inertial mass is:

a. 2:1

b. 1:1

c. 1:2

d. 4:1

155. Where does a body weigh maximum?

a. Equator

b. moon

c. at poles

d. None of above

156. To determine time, an astronaut in an earth satellite should use:

a. Either a spring watch or a pendulum clock

b. A spring watch

c. Neither a spring watch nor a pendulum clock

d. None of above

157. On moving from poles to equator, the weight of body:

a. Constantly decreases

b. Constantly increases

c. remains constant

d. Sometimes increases or sometimes decreases

158. A boy is playing on a swing in sitting position. The time period of oscillation of swing is T. If the boy stands up, the time period of swing will be:

a. Less than T

b. More than T

c. Equal to T

d. Cannot be predicted

159. Objects A and B are separated by small distance r . The magnitude of force of gravity on A from B is given by and the magnitude of the force of gravity on B from A is . If the mass A is doubled while that of B is unchanged, then:

a. will double while will remain the same

b. Both and will double

c. will double while will remain the same

d. Both and remain same

160. Newton’s law of gravitation is valid :

a. all bodies

b. for small bodies

c. for large bodies

d. for heavenly bodies

161. The gravitational mass of a body is M. The inertial mass of same body on moon will be:

a. M

b. zero

c. 6M

d. M/6

162. A tunnel is dug along one of the diameters of earth. The force on particle of mass m distant x from center in this tunnel will be:

a. $\frac{GMm}{R^2x}$

b. $\frac{GMmR^2}{x}$

c. $\frac{GMm}{R^2}$

d. $\frac{\mathbf{GMm}}{\mathbf{R}^\mathbf{3}}$

163. The length of day from today when the sun is directly overhead till tomorrow again when sun is directly overhead can be determined by:

a. rotation of earth about its own axis

b. rotation of earth about its own axis as well as its revolution around sun

c. revolution of earth around sun

d. Inclination of axis of rotation of earth from the plane of revolution

164. At what angle with the horizontal should a projectile be fired with escape velocity to enable it from gravitational pull of earth?:

a. at any angle

b. less than 45^o

c. greater than 45 ^o

d. 45^o

165. The orbital speed of Jupiter is:

a. Less than orbital speed of earth

b. Greater than orbital speed of earth

c. Equal to the orbital speed of earth

d. All of above

166. A force of 75 N acts on a body of mass 2.5 kg at central point. The intensity of gravitational field at this point will be:

a. 13 N/kg

b. 30N/kg

c. 20N/kg

d. 40N/kg

167. The length of a simple pendulum for a given time period is I. If the pendulum is taken to a place where acceleration due to gravity is doubled, then for time period to remain the same its length should be:

a. 2I

b. I

c. I/2

d. I/4

168. The weight of a body at center of earth will be:

a. mg

b. mg/2

c. zero

d. infinity

169. If the density of earth is doubled keeping its radius constant then acceleration due to gravity ‘g’ will be:

a. m/s²

b. 9.8m/s²

c. 4.9 m/s²

d. Cannot be predicted

170. A stone is dropped freely into a tunnel along diameter of earth , when it reaches the center of earth then it possesses only:

a. weight

b. Mass

c. Kinetic energy

d. b & c

171. The acceleration due to gravity in a hole dug into non- uniform spherically body:

a. will increase as you go deeper, reaching a maximum at the center

b. will increase as you go deeper , but eventually reach a maximum , and then decrease until you reach the center

c. can increase or decrease as you go deeper

d. must decrease as you go deeper

172. A planet of mass M is revolving round the sun is an elliptical orbit. If its angular momentum is L, then area swept per second by the joining planet to sun will be:

a. LM/2

b. L/M

c. L/2M

d. None of above

173. Jumps from 5^th storey of building with load of mass m on head. The weight experienced by him before reaching the earth will be :

a. mg/2

b. m(g +a )

c. mg

d. Zero

174. A body of mass 5kg is hanging from a spring balance inside a lift. If the lift is moving downwards with an acceleration of 10m/s², then the reading of spring balance will be :

a. 20 kg

b. 10 kg

c. Zero

d. None of above

175. If orbital speed of moon is increased by 41.1% then moon will:

a. fall on earth

b. leaves its orbit and escape out

c. have time period equal to 27 days

d. Attract all bodies on earth between it

176. Project star shine is an expensive satellite launched to involve school children in orbit observations. As the satellite encountered friction from the earth’s atmosphere the radius of the near circular orbit lowly decreased over period of many months. As the radius of the orbit decrease, the kinetic energy of the satellite :

a. increase

b. decrease

c. remain the same

d. none of above

177. The gravitational effect of which of following causes tidal waves in the sea? :

a. sun

b. earth

c. moon

d. all of above

177. A satellite is orbiting around earth with period T. If the earth suddenly shrinks to half its radius without change in mass, the period of revolution of satellite will be:

a. equal to T

b. 2T

c. T/2

d. Insufficient data to reply

178. If the earth stops rotating in its orbit about sun, there will be variation in weight of bodies at:

a. latitude

b. poles

c. equator

d. nowhere

179. A ring has mass M and radius R. The force experienced by a point mass m will be maximum when it is placed:

a. at center of ring

b. at R from center of ring along axis

c. at R from center along axis

d. None of above

180. The mass of a body on surface of earth is 6kg. If we measure the mass on surface of moon, it will be:

a. 6kg

b. 1kg

c. 36 kg

d. 0.1 kg

181. The gravitational force of earth on a ball of mass 1kg is 9.8 N. The attraction of ball on earth is:

a. more than9.8N

b. 9.8N

c. Cannot be predicted

d. Slightly less than 9.8N

182. The gravitational potential inside a spherical shell is:

a. equal to that on surface

b. greater than that on surface

c. Zero

d. less than on surface

183. Gravitational forces are:

a. Strong

b. Short range

c. Weak

d. non-central

184.A spherical symmetric non-rotating body has a density that varies appreciably with radical distance from the center of the body the acceleration of the free fall is:

a. definitely larger than zero

b. possibly larger than zero

c. definitely equal to zero

d. None of above

185. The variation in the speed of planets in their orbits about the sun can be explained on the basis of law of conservation of:

a. Total energy

b. Linear momentum

c. angular momentum

d. angular kinetic energy

186. The force required to keep the satellite in orbit is provided by:

a. Electrostatic attraction

b. Electromagnetic force

c. Gravitation

d. terminal velocity

187. If total energy of a particle is negative but not minimum, the path is::

a. Circular

b. Hyperbolic

c. elliptical

d. parabolic

188. If a body of 80 kg is allowed to fall freely, its weight becomes:

a. 49N

b. 490N

c. 50N

d. Zero

189. Satellites are put into orbits :

a. rockets

b. aero planes

c. missiles

d. all of above

190. Suppose the earth were a hallow sphere. The intensity of gravitational field inside it in the empty space will be:

a. more than 9.8N/kg

b. less than 9.8N/kg but not zero

c. Zero

d. 9.8N/kg

191. Consider a spherically symmetric planet with a mass density that varies as a function of distance from the center of the planet. The magnitude of the gravitational potential energy of the system of the planet and a test mass would be:

a. Zero at the center, and the maximum value would occur at the surface of the planet.

b. non-zero at the center, and the maximum value would occur at the surface of the planet

c. non-zero at the center, but the maximum value would occur at the same point beneath the surface but away from the center

d. non-zero at the center, but the maximum value would occur at the center.

192. A body under inverse square force will move along a circular path if total energy is:

a. positive

b. Negative but equal to minimum potential E

c. Zero

d. negative but greater than minimum potential E

193. The minimum velocity required to put a satellite into orbit is called:

a. critical velocity

b. linear velocity

c. angular velocity

d. tangential velocity

194. In comparison, Einstein theory of gravitation is_________ than that of Newton gravitation theory:

a. Better

b. Not better

c. Better up to some extent

d. None of above

195. Gravitational potential energy is _________ quantity:

a. Scalar

b. Vector

c. Universal

d. None of above

196. If the earth stops spinning about its axis, weight of body will increase at:

a. latitude

b. poles

c. equator

d. Both a & b

197. A body of 2kg is suspended from ceiling of an elevator moving up with an acceleration g, its apparent weight in elevator will be:

a. 9.8N

b. 19.6N

c. 39.2N

d. 129.4

198. How many days would be in year if distance between earth and sun were reduced to half of its present value(assuming circular orbit):

a. 365 days

b. 730days

c. 129days

d. none of above

199. If we whirl a stone at the end of a string in vertical circle, it is likely to break when the stone is

a. At the highest point

b. At any point during motion

c. at lowest point

d. all of above

199. Objects A and B are separated by small distance r . The magnitude of force of gravity on A from B is given by and the magnitude of the force of gravity on B from A is . If the mass A is doubled while that of B is halved, then:

a. will double while will remain the same

b. Both and will double

c. will double while will remain the same

d. Both and remain same

200. Project star shine is an expensive satellite launched to involve school children in orbit observations. As the satellite encountered friction from the earth’s atmosphere the radius of the near circular orbit lowly decreased over period of many months. As the radius of the orbit decrease, the total energy of the satellite :

a. increase

b. decrease

c. remain the same

d. none of above

201. Project star shine is an expensive satellite launched to involve school children in orbit observations. As the satellite encountered friction from the earth’s atmosphere the radius of the near circular orbit lowly decreased over period of many months. As the radius of the orbit decrease, the age speed of the satellite :

a. increase

b. decrease

c. remain the same

d. none of above

MCQ's with Answers

1. A vector is represented graphically by a directed line according to suitable scale with:

2. The direction of a vector in space is specifiaed by the:

3. If a vector makes an angle with x-axis, then its x-component is:

4. If position two aeroplanes at any instant in given by (2, 3,4) and (5,6,7) from origin in kilometres, then distance between position of two aero planes will be:

5. If resultant vector lies in 2nd quadrant, then its direction is;

6. Two forces act together on an object, then magnitude of their resultant is maximum when angle between forces is:

7. The resultant of magnitude of two forces 6N and 8N acting at right angle to each other is:

8. The magnitude of resultant of two forces acting at right angle to each other is:

9. When two forces of equal magnitude make an angle of with each other, then magnitude of their resultant is:

10. If resultant of two vectors each of same magnitude is also of same magnitude, then angle between them is:

11. The example of vector product is:

12. The vector product of anti-parallel vectors is:

13. Vector product of with itself is:

14. The magnitude of is equal to area of ____________ with as its adjacent sides:

15. Half of magnitude of is equal to area of ­­­­­­­­­­­_____________ with as its adjacent sides:

16. If points along x-axis, then must lie in:

17. A particles starts from center O towards OA, then moves along AB and stops at B. If the displacement of particle is:

18. Mark the wrong statement:

19. The position vector of a particle moving along a curve in cylindrical polar coordinates is:

20. Three coplanar forces acting on a body keep it in equilibrium. This should therefore be:

21. A unit vector in terms of direction cosines can be written as:

22. Three unit vectors are:

23. The direction of is always:

24. Derivative of velocity with respect to time is called:

25. The vector field is solenoidal if:

27. If vector field can be expressed as gradient of a scalar ф, then vector field is known as:

30. The divergence of curl of a vector is always equal to:

31. The curl of gradient of a scalar is always equal to:

32. The linear integral of a vector field is equal to:

33. The volume integral of divergence of a vector field is equal to:

34. For a conservative field :

35.If a vector makes an angle with x-axis, then its y-component is:

36. If are perpendicular to each other, then:

37. Example of scalar product is:

38. Two vectors and are making an angle with each other , then scalar projection of on is:

39. The rain is vertically with a speed 4m/s and the man is moving due east with speed 3m/s. With what speed, the rain appears to be coming to man?

40. The direction of vector product can be found by_______ rule:

42. Which of the following group represents vector only;

45. A fluid that has non-vanishing curl is called:

46.Electric field is an example of;

47. Grads has direction in which S changes most rapidly and its magnitude is _________ derivative of S :

48. Scalar product of differential operator ∇ with itself is called:

49. Relation between surface and line integrals is given by;

50. A particle moves along the circular path with constant speed. What is nature of its acceleration?

51. A simple pendulum hangs from ceiling of a train. The string is included towards the rear of the train What is nature of motion of train:

52. A particle moves in a plane with acceleration having direction different than that of the instantaneous velocity. What is nature of trajectory:

53. A particle travels according to the equation, x=acosωt & y=bcos(ωt + 45o) The trajectory is,

54. A passenger travelling in a train moving with constant velocity drops a stone from window. To the passenger the path of stone will be;

55. The time Elapsed is plotted along x-axis and acceleration is plotted along y-axis. The area between graph and x-axis is gives:

56. The angular speed of minute hand of clock in degrees per second is:

57. The angular acceleration of a particle moving along a circle with uniform speed is:

58. A stone of mass m tied to a string of length ‘l’ is rotated in a circle with the other end of string as the center. The speed of stone is ‘v’. If sting breaks, the stone will move:

59. A bottle of soda water is held by the neck and swing briskly in a horizontal circle. Near which position of the bottle do the bubbles collect:

60. A car is taking a turn on a level road. It may be thrown towards because of the:

61. An automobile is turning a circular road radius ‘r’. The coefficient of friction between the tyres and road is ‘µ ’. The velocity of vehicle should not be more than

62. A particle moves according to equation , retardation at any instant is:

63. A bus is standing at bus stop. A man is in front of bus stop. Suddenly the bus starts moving with an acceleration 2m/s2. The man notices the bus moving after 2s of its motion. With what constant speed man should run so as to get in the bus in 2s when he notices the bus moving:

64. The displacement of particle moving in one direction is, x is in meters and t is in seconds. The displacement when velocity is zero:

65. Which of the following can be zero when a particle is in motion for some time?

66. The velocity time graph of motion stating from rest with uniform acceleration is a straight line:

67. If a distance covered by a particle is zero, then what we can say about its displacement:

68. A bucket is placed in the open where the rain is falling vertically. If wind begins to blow at double the velocity of rain, how will the rate of filling of bucket change :

70.The slop of velocity time graph for uniform motion is:

72. Suppose net force on an object is zero, which of the following could be constant:

73. Rain drops fall with constant velocity. This suggests:

74. Rain is falling vertically downwards. To a man running eastward, the rain will be appear to coming from:

75. A moving body is covering the distance directly proportional to the cube of time. The acceleration of body is:

76. A stone is thrown upward which rises to a height of 100m. The relative velocity of stone with respect to earth will be maximum at:

77. A ball is thrown horizontally from top of tower. What happens to horizontal component of velocity?

78. A projectile is thrown at an angle of with horizontal and its range is . Another projectile is thrown at an angle of with vertical and its range is . The relation between is:

79. An object is projected upwards. Its acceleration at highest point is:

80. If a man wants to hit a target, he should aim his rifle in a direction:

81. A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of mud are thrown:

82. A block of metal is lying on the floor of bus. Maximum acceleration which can be given to the bus so that the block remain may at rest, will be:

83. A body moving in a circular motion with constant speed has:

84. A body moving in a circular motion with constant speed has:

85. Two racing cars of masses are in circles of radii respectively. Their speeds are such that each makes a complete circle in the same length of time t. The ratio of angular speed of the 1st and 2nd car is:

86. If the earth were to rotate faster than its present speed, the weight of an object will:

87. A pendulum is clapped on the roof a stationary car and its time period is T. If car starts to move with acceleration a then its time period will be:

5. If resultant vector lies in 2^nd quadrant, then its direction is;

15. Half of magnitude of is equal to area of _____________ with as its adjacent sides:

53. A particle travels according to the equation, x=acosωt & y=bcos(ωt + 45^o) The trajectory is,

63. A bus is standing at bus stop. A man is in front of bus stop. Suddenly the bus starts moving with an acceleration 2m/s². The man notices the bus moving after 2s of its motion. With what constant speed man should run so as to get in the bus in 2s when he notices the bus moving:

85. Two racing cars of masses are in circles of radii respectively. Their speeds are such that each makes a complete circle in the same length of time t. The ratio of angular speed of the 1^st and 2^nd car is:

111. A block of mass m is taken to a height R_e/2. The work done is:

131. The expression [ML²T^-2 ] represents:

132. A Force F is given by F= at + bt², where t is time. The dimension of a and b are: