Team Quanta gladly presents all possible short questions of BS Physics book Mechanics – I’s Chapter#02: Particle Dynamics for the ease of students.
Q.1 In canonical pendulum what happens to the period and speed when ?
Answer: Speed of canonical pendulum is given by;
$v= \sqrt{gRtan\theta}$
For $\theta=0^o$ v=$\sqrt{gRtan0}= 0$
Time period of canonical pendulum is
$$T= 2\pi\sqrt{\frac{Lcos\theta}{g}}$$
For $T= 2\pi\sqrt{\frac{L}{g}}$, it becomes a simple pendulum.
Q.2 How does earth’s rotation affect the apparent weight of an object at the equator?
Answer: As value of g decreases, so weight of object decreases.
Q.3 You may feel scared at the top of the roller coaster ride in the amusement parks but you never fall down even when you are upside down?
Answer: We do not fall down even when we are upside down due to the centripetal force which is acting on us. This force keeps us safe from falling down.
Q.4 Why are banked tracks needed for turns?
Answer: Banked tracks are needed for turns that are taken so quickly that friction alone cannot provide necessary centripetal force.
Q.5 In which direction does mud fly off the tyre of a moving car and why?
Answer: The force of adhesion between tyre and mud supplies centripetal force. The force which appears due to the rotatory motion of wheel becomes large enough at particular speed and mud start flying off along tangent to the wheel.
Q.6 If we know the position vectors of a particle at two points along its path and also know the time interval during which it moved from one point to the other, can we determine the instantaneous velocity of particle and average velocity?
Answer: We cannot find the instantaneous velocity because the points could be separated by a finite displacement. We can find the average velocity by the relation,
$$v_{av} = \frac{\Delta x}{\Delta t}$$
Q.7 Why do we wear the seat belts?
Answer: When a moving car stops suddenly, the passengers move forward towards the windshield. Seat belts change the force of motion and prevent passengers from moving. Thus the chance of injury is reduced to certain limit.
Q.8 Why do we keep our legs far apart when we have to stand on the floor of a moving train?
Answer: In order to produce state of stability we keep our legs far apart. Thus center of gravity will lie in middle of body to keep it in stable equilibrium.
Q.9 Why earth does not fall toward sun because of its attraction?
Answer: The force of attraction provides the centripetal force and earth moves in stable orbit with a velocity perpendicular to the force, so it does not fall.
Q.10 Explain whether or not the following particles have acceleration:
Answer: (a)- a particle moving in a straight line with constant speed has no acceleration .(b) Since the particle is continuously changing the direction of its velocity, so it has acceleration.
Q.11 Give two examples of velocity dependent forces.
Answer: Examples of velocity dependent forces are given below:
- Projectile motion is an example of velocity dependent force. When a projectile is projected over a long distance, its motion does not follow equations of motion. This is because as speed becomes long distance, its motion does not follow equations of motion. This is because as speed becomes larger, the drag force increases with speed.
- Drag force moving through a medium such as water changes with velocity of object.
Q.12 Can an object exert a force on itself? Explain your answer.
Answer: No, an object cannot exert a force on itself. If it could, then objects would be able to accelerate themselves, without interacting with the environment.
Q.13 If the reaction and action forces are always equal in magnitude and opposite in direction to each other, then doesn’t the net vector force on any object and necessarily add up to zero? Explain.
Answer: The resultant force doesn’t add up to zero on any object necessarily because if it were zero, then any object cannot be accelerated. If we choose a single object as our system, action and reaction forces can never add to zero, as they act on different objects.
Q.14 A child tosses a ball straight up. He says that the ball is moving away from his hand because the ball feels an upward “force of the throw” as well as the gravitational force, (a) Can the “force of the throw” exceed the gravitational force? (b) Why does the ball move away from the child’s hand?
Answer: (a) If there were a “force of throw” experienced by the ball after it leaves the hand and the force exceeded the gravitational force, the ball would accelerate upward, not downward. If the “force of the throw” equals the gravitational force , the ball would move upward with a constant velocity, rather than slowing down and coming back down.
(b) The ball moves away from the hand because the hand imparts a velocity to the ball and then the hand stops moving.
Q.15 Give one example each of variable acceleration due to change in magnitude, direction and both in magnitude and direction.
Answer: A body executing simple harmonic motion has variable acceleration due to change in magnitude.
A body in uniform circular motion has variable acceleration due to change in direction called centripetal acceleration.
A body moving along elliptical path has a variable acceleration due to both change in magnitude and direction.
Q.16 Does the average velocity give any information about path followed? Explain.
Answer: No, for example when a squash ball comes after bouncing the wall several times, its average velocity is zero where as instantaneous velocity is not zero.
Q.17 Can a velocity of an object reverse direction when acceleration is constant? If yes, give an example. If not prove it.
Answer: Yes, for example when a stone is thrown upward, its velocity goes on decreasing and becomes zero at maximum height. For downward flight, velocity is reversed but acceleration remains constant.
Q.18 Does the direction of circular motion change continuously?
Answer: Yes, direction of motion changes continuously in a circular path.
Q.19 Can centripetal force and centrifugal reaction balance each other?
Answer: No, since centripetal force and centrifugal reaction are action and reaction forces, they do not balance each other as they act on two different bodies. Only forces acting on same body can balance each other.
Q.20 Describe how a driver can steer a car travelling at constant speed so that the acceleration is zero or the magnitude of the acceleration remains constant.
Answer: A driver can steer a car with a zero acceleration on a straight level road that does not curve to left or right.
A driver can steer a car with a acceleration having a constant magnitude either in circle or straight ahead on a level road.
Q.21 A car is travelling toward east. Can it have a velocity east and at same time have acceleration toward west?
Answer: A car is travelling toward east does not have velocity toward west. If brakes are applied, the car decelerates having velocity still towards east, but radiation will be towards west.
Q.22 Do objects of different weights fall with same acceleration on the earth?
Answer: Yes objects of different of weights fall with same acceleration at the surface of the earth, in situations air friction is negligible.
Q.23 Consider a small raindrop and a large rain drop falling through the atmosphere. Compare their terminal speeds. What are their accelerations when they reach terminal speed?
Answer: In case of spheres, the terminal speed is proportional to the square of the radius, so the larger drop has higher terminal speed. When moving with terminal speed, an object is in equilibrium and has zero acceleration.
Q.24 What force cause (a)-an automobile, (b)-a propeller driven airplane, and (c)-a rowboat to move?
Answer: a) A force of friction exerted by the road where it meets the rubber tires accelerates the ccar forward.
b)-The around the propeller pushes forward on its blades.
c)-The water pushes the blade of the oar toward the bow.
Q.25 What prevents the rain drop from acquiring a large enough velocity?
Answer: The presence of air exerts a drag force on the falling drop. This drag force reduces the net downward force on drop and thus prevents the drop from obtaining a large enough speed.
Q.26 The fog droplets appear to be suspended in air. Why?
Answer: As the fog droplet falls, the drag force acting on it becomes equal to weight of droplet, then net force acting on it is zero. Thus the droplet will fall with terminal velocity whose value is very small. So droplet falls so slowly that it appears to be suspended in air.
Q.27 A bomber drops its bomb when it is vertically above the target, it misses the target. Why?
Answer: If bomb is dropped when bomber is vertically above target, it will strike a point ahead of target due to horizontal component of velocity. As such bomb missed target.
Q.28 In long jump what factors determine the span of jump? OR Why an athlete starts running before he takes jump?
Answer: Span of jump is given by range of projectile,
$$R=\frac{v_0^2\sin{2\theta}}{g}$$
Hence span of jump depends upon angle of projection. That is why an athlete starts running before he takes the jump.
Q.29 A pail of water can be whirled in a vertical path such that no water is spilled. Why does the water stay in the pail, even when the pail is above your hand?
Answer: The water stay in the pail due to inertia. The water tends to move along a straight line, but the bucket pulls it in and around in a circle.
Q.30 How can a projectile you throw so that it has zero speed at the top of trajectory? How can a projectile you throw so that it has non zero speed at the top trajectory?
Answer: If a projectile is thrown straight upward, then it has zero speed at top of trajectory.
If projectile is thrown at any angle other than 90° to horizontal, it has non zero speed at top of trajectory .
Q.31 Why does a pilot tend to black out when pulling out of a steep dive?
Answer: A pilot tends to black out when pulling out of a steep dive because the gravitational force and centripetal force cannot be balanced by his blood pressure.
Q.32 If a projectile is thrown horizontally away from a cliff. Is this projectile a freely falling body?
Answer: Yes, it is freely falling body, because force acting on it is only gravity.
Q.33 Your hands are wet, and the restroom towel hanger is empty. What do you do to get drops of water off your hands? How does the motion of the drops exemplify one of Newton’s laws?
Answer: Since force of static friction is not large enough to keep the water stationary with respect to the skin at large acceleration. So the water slides along the skin surface and reach the end of a finger and then slides off into the air. This is an example of Newton’s first law in action that the drops continue in motion while the hand is stopped.
Q.34 Describe the path of a moving body in the event that its acceleration is constant in magnitude at all the times and perpendicular to the velocity and its acceleration is constant in magnitude at all times and parallel to the velocity.
Answer: When acceleration is constant in magnitude at all times and perpendicular to the velocity, then body will move in a circle at a constant speed.
When acceleration is constant in magnitude at all times and parallel to the velocity, then body will move in a straight line with variable speed.
Q.36 At what point or points in its trajectory, a projectile has maximum speed and minimum speed?
Answer: Speed of projectile is minimum at highest point and maximum at point of projection and at point where it hits ground.
Q.38 If someone told you that, astronauts are weightless in orbit because they are beyond the pull of gravity, what is your opinion about this statement?
Answer: This statement seems to be incorrect because astronauts are moving in circular orbits because of gravitational pull of earth.
Q.39 If the earth were cease rotating about its axis what will be the change in the value of g at a place of altitudes 45° assuming the earth to be sphere.
Answer: If g is acceleration due to gravity when earth is at rest and is acceleration when earth is rotating with angular velocity , then
$$g^\prime = g-R\omega^2 cos^2 45^o$$
$$g – g^\prime =6.38 \times 10^8 cm \left ( \frac{2\pi }{60 \times 60 \times 60} \right ) cos^2 45^o \rightarrow g – g^\prime = 1.686 cm / s^2$$
Q.40 A rubber ball is dropped onto the floor. What force causes the ball to bounce?
Answer: The resultant of all the forces between molecules is the force that cause the ball to bounce.
Q.41 A falling sky driver reaches terminal speed with his parachute closed. After the parachute is opened, what parameters change to decrease this terminal speed?
Answer: The drag force is proportional to the square of speed and to the effective area of the falling object. At terminal velocity, the drag and gravity forces are equal. When the parachute opens, then its effective area increases and hence the drag force to increases. The greater drag force causes the speed to decrease.
Q.42 An object executes circular motion with constant speed whenever a net force of constant magnitude acts perpendicular to the velocity. What happens to the speed if the force is not perpendicular to the velocity?
Answer: When force is not perpendicular to velocity, the tangential force component causes tangential acceleration and speed changes.
Q.43 How Coriolis force owes its existence to the motion of particle with respect to a rotating frame of reference?
Answer: Coriolis force is given by,
$$F_{cor} = -2m \vec{\omega} \times \vec{v_r}$$
where “$\vec{v_r}\prime$ ” is velocity of the particle with respect to rotating frame. Obviously it will be zero if particle is at rest relative to rotating frame of reference. Thus Coriolis force owes its existence to the motion of particle with respect to rotating frame of reference.
Q.44 A man most likely has been in an elevator that accelerates upward as it moves toward a higher floor. In this case, he feels heavier. In fact he is standing on a bathroom scale at the time, the scale measures a force having a magnitude that is greater than his weight. Therefore, he has tactile and measured evidence that leads him to believe he is heavier in situation. Is the man heavier?
Answer: In fact weight is unchanged. The said experiences are due to being in a reference frame. To provide the acceleration upward , the floor or scale must exert on his feet an upward force that is greater in magnitude than his weight. It is this greater force he feels , which we interpret as feeling heavier. The scale reads this upward force, not his weight, and so its reading increases.
Q.45 A hunter fires directly at the monkey hanging on the branch of a tree. The monkey drops instantly as he sees the bullet leaving the gun. Who is the clever of two?
Answer: if monkey makes a jump during fire, the bullet will hit him due to projectile motion. If monkey sticks to branch of tree, it would have acted clever than hunter. On the other hand , the hunter should aim monkey a little above actual position held by monkey so that bullet hits monkey.
Q.46 What will be the direction of Coriolis force in northern and southern hemispheres?
Answer: In northern hemisphere a moving body turns towards right and in southern hemisphere a moving body will turn towards left due to effect of Coriolis forces.
Q.47 Can a particle be in equilibrium in non- inertial frame?
Answer: A particle can be in equilibrium in a non inertial frame when the external force acting on it is equal and opposite to fictitious force due to non-inertial frame.
Q.48 Describe a situation in which moving car can have a centripetal acceleration but no tangential acceleration.
Answer: A moving car in a circle at a constant speed has centripetal acceleration but tangential acceleration.
Q.49 What is angle between velocity and acceleration at the highest point in the projectile motion?
Answer: At highest point velocity is only horizontal for a projectile i.e. tangent to curve and acceleration is vertically downward. So its acceleration and velocity are perpendicular to each other.
Q.50 If the acceleration of the particle remains constant in magnitude but not in direction,is its path necessarily a straight line?
Answer: No, when acceleration has constant magnitude , but variable direction, then particle moves along circular path.
Q.51 Motion with constant velocity is special case of motion with constant acceleration. Is this statement true? Explain.
Answer: Yes when body moves with uniform velocity, then change in velocity is zero and acceleration is also zero.
Q.52 Can there be a acceleration when a body is moving with constant speed? If yes, given an example. If not prove it.
Answer: Yes, for example when a body is moving along a circular path with constant speed , it will have acceleration due to change of direction at every point.
Q.53 Give two examples in which the force of friction exerted on an object is in the direction of motion of the object.
Answer: Example1; When we pull away from a stoplight, friction exerted by the ground on the tires of the car accelerates the car forward.
Example2; As we begin running forward from rest, friction exerted by the floor on our shoes causes our acceleration.
Q.54 Why roads are banked in hill stations?
Answer: In hill stations roads are banked since only frictional force is not sufficient to provide necessary centripetal force to take the turn at fast speed.
Q.55 Why a cyclist tilts inward while taking a turn around the corner?
Answer: While taking a turn round a curve , the cyclists tilts inwards to obtain necessary centripetal force which is provided by friction between road and tyre.
Q.56 A man sitting in a bus moving with constant acceleration throws a ball straight up in air. Where does the ball fall?
Answer: During the flight of ball, the man is carried forward due to acceleration of bus. This acceleration is not transferred to the ball an consequently it falls behind the man.
Q.57 A projectile is launched at some angle to the horizontal with some initial speed v0 and air resistance is negligible. (a) Is the projectile a freely falling body?(b) What is acceleration in the horizontal and vertical directions?
Answer: (a) Yes, the projectile is in free fall.
(b) Its horizontal component of acceleration is zero and vertical component of acceleration is the downward acceleration of gravity.
Q.58 Why it is difficult to take the turn for a car at high speed on a level road?
Answer: As centripetal force is proportional to square of velocity, so centripetal force must be large at high speed which is difficult to achieve and it becomes difficult to turn.
Q.59 A spacecraft drifts through space at constant velocity. Suddenly, a gas leak in the side of the spacecraft gives it a constant acceleration in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of velocity. What is the shape of the path followed by the spacecraft in this situation?
Answer: In this case the velocity is constant in the horizontal direction and there is a constant acceleration in the perpendicular direction. Therefore, a curve of the parabola shape ( projectile trajectory ) is observed.
Q.60 When a car is travelling due westward with a constant speed of 20m/s, what is the resultant force acting on it?
Answer: As the acceleration is zero, so the resultant force is zero.
Q.61 Suppose someone is driving a classical car. Why should he avoid slamming on his brakes when he wants to stop in the shortest possible distance?
Answer: If he slams on the brake, tires of car will skid on the road because the force of kinetic friction between the tires and the road is less than the maximum static friction force.
Q.62 Identify action-reaction pairs in the following cases: (a) a man takes a step (b) a snowball hits a man in the back (c) a base ball player catches a ball (d) a gust of wind strikes a window.
Answer: (a) The action force is the force his foot exerts on the Earth; the reaction is the force of Earth on his foot.
(b) The action force is the force exerted on the man’s back by the snowballs; the reaction is the force exerted on the snowball by the man’s back.
(c) The action force is the force of glove on the ball; the reaction is the force of the ball on the glove.
(d) The action force is a force exerted on the window by the air molecules; the reaction is the force on the air molecules exerted by the window.
