Question 1

You are driving a motorcycle on a horizontal road. It is moving with a uniform velocity. Is it possible to accelerate the motorcycle without putting higher petrol input rate into the engine?

Accepted Answer

Yes, it is possible to accelerate the motorcycle without putting higher petrol input rate into the engine by driving the motorcycle on a circular track.

Question 2

Some washing machines have cloth driers. It contains a drum in which wet clothes are kept. As the drum rotates, the water particles get separated from the cloth. The general description of this action is that "the centrifugal force throws the water particles away from the drum". Comment on this statement from the viewpoint of an observer rotating with the drum and the observer who is washing the clothes.

Accepted Answer

The person rotating with the drum will observe that centrifugal force and coriolis force act on the water particles and the person washing the cloth will observe that water particles are thrown outward (away from the drum) and no pseudo force is acting on the particles.

Question 3

A small coin is placed on a record rotating at 3331​ rev/minute. The coin does not slip on the record. Where does it get the required centripetal force from ?

Accepted Answer

The coin gets the required centripetal force from the frictional force between the coin and the record.

Question 4

A bird while flying takes a left turn, where does it get the centripetal force from ?

Accepted Answer

The bird tilts its body and tail in such a way that the air around offers a dragging force in left direction, perpendicular to its initial direction of motion. This dragging force provides the necessary centripetal force to take the left turn.

Question 5

Is it necessary to express all angles in radian while using the equation ω = ω0​  + at ?

Accepted Answer

No, it is not necessary to express all the angles in radian while using the equation ω = ω0​  + at.If ω (angular velocity) and α (angular acceleration) are in rad/s and rad/s2, respectively, we will get the angle in radian.

Question 6

After a good meal at a party you wash your hands and find that you have forgotten to bring your handkerchief. You shake your hand vigorously to remove the water as much as you can. Why is water removed in this process?

Accepted Answer

While shaking, our hand moves on a curved path with some angular velocity and water on our hand feels centrifugal force in the outward direction. Therefore, water get detached from our hand and leaves it.

Question 7

A smooth block loosely fits in a circular tube placed on a horizontal surface. The block moves in a uniform circular motion along the tube. Which wall (inner or outer) will exert a nonzero normal contact force on the block?

Accepted Answer

The outer wall will exert a non-zero normal contact force on the block. As the block moves in a uniform circular motion, centrifugal force in radially outward direction acts on it and it comes in contact with the outer wall of the tube.

Question 8

Consider the circular motion of the earth around the sun. Which of the following statements is more appropriate ?(a) Gravitational attraction of the sun on the earth is equal to the centripetal force.(b) Gravitational attraction of the sun on the earth is the centripetal force.

Accepted Answer

(a) Gravitational attraction of the Sun on the Earth is equal to the centripetal force. This statement is more appropriate.Gravitational attraction of the Sun on the Earth provides the necessary centripetal force required for the circular motion of the Earth around the Sun.

Question 9

A car driver going at some speed v suddenly finds a wide wall at a distance r. Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?

Accepted Answer

As the wall is at a distance r, the driver should either take a circular turn of radius r or apply brakes to avoid hitting the wall.

Question 10

A heavy mass m is hanging from a string in equilibrium without breaking it. When this same mass is set into oscillation, the string breaks. Explain.

Accepted Answer

When the same mass is set into oscillation, the tension in the string increases because of the additional centripetal force of the mass oscillating in a curved path.

Question 11

When a particle moves in a circle with a uniform speed:

Accepted Answer

(d) Its velocity and acceleration both change.In a circular motion, the direction of particle changes. Therefore, velocity, being a vector quantity, also changes.As the velocity changes, acceleration also changes.

Question 12

Tow cars having masses m1​ and m2​ moves in circles of radii r1​ and r2​ respectively. If they complete the circle in equal time, the ratio of their angular speed ω1​/ω2​ is:

Accepted Answer

(d) 1.Time period (T) is same for both the cars.We know that :ω∝T1​So,ω2​ω1​​=1

Question 13

A car moves at a constant speed on a road as shown in figure. The normal force by the road on the car NA and NB when it is at the points A and B respectively.

Accepted Answer

(c) NA​<NB​.From the figure in the question, it is clear that rB​>rA​.Here, normal reaction is inversely proportional to the centrifugal force acting on the car, while taking turn on the curve track. Also, centrifugal force is inversely proportional to the radius of the circular track.Therefore, we have: NA​<NB​.

Question 14

A particle of mass m is observed from an inertial frame of reference and is found to move in a circle of radius r with a uniform speed v. The centrifugal force on it is:

Accepted Answer

(d) Zero.The centrifugal force is a pseudo force and can only be observed from the frame of reference, which is non-inertial w.r.t. the particle.

Question 15

A particle of mass m rotates with a uniform angular speed ω. It is viewed from a frame rotating about the Z-axis with a uniform angular speed ω0. The centrifugal force on the particle is:

Accepted Answer

(b) mω02​ a .The centrifugal force on the particle depends on the angular speed (ω0) of the frame and not on the angular speed (ω) of the particle. Thus, the value of centrifugal force on the particle is  m ω02​ a .

Question 16

A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s2. The particle is now shifted to a new position to make the radius half of the original value. The new value of the speed and acceleration will be:

Accepted Answer

(a) 10cm/s,10cm/s2.It is given that the turntable is rotating with uniform angular velocity. Let the velocity be  ω .We have:v=rω⇒v∝r(P for constant ω)v′v​=r′r​⇒v′=2v​=10 cm/sSimilarly, we have: a′=2a​=10 cm/s2

Question 17

Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position.

Accepted Answer

(c) mg is not greater than rmv2​ .At the top of the path, the direction of mg is vertically downward and for centrifugal force (rmv2​) ,  the direction is vertically upward. If the vertically downward force is not greater, water will not fall.

Question 18

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

Accepted Answer

(c) Along a tangent.The stone will move in a circle and the direction of velocity at any instant is always along the tangent at that point. Therefore, the stone will move along the tangent to the circle at a point where the string breaks.

Question 19

A coin placed on a rotating turntable just slips. If it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of:

Accepted Answer

(d) 8 cm.

Question 20

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it:

Accepted Answer

(a) Increases.The normal force on the motorcycle , N = mgcosθ−Rmv2​As the motorcycle is ascending on the overbridge, θ decreases (from 2π​ to 0).So, normal force increases with decrease in θ.

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