Answers to Problems on (Circular Motion) HC Verma's Questions for Short Answer

 Q#1

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

Answer:   
Yes. Since acceleration is the rate of change of velocity and velocity can even be changed by changing its direction keeping the magnitude constant.

So, keeping the the petrol input rate constant if the motorcycle is turned along an arc of circle it will have an acceleration towards the center of arc.      

Q#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.  

Answer: 
From the view point of an observer rotating with drum his frame of reference is non-inertial as it has a centripetal acceleration. To apply Newton's Laws in this frame a pseudo force has to be applied on the particle which amounts to mass multiplied by the acceleration of the frame but the direction is just opposite to the acceleration of the frame. This pseudo force is called (Centrifugal force).
So, from observer's viewpoint rotating with drum this statement is true.

But from the observer's viewpoint who is washing the clothes this statement is not true as his frame is inertial and in inertial frame there is no pseudo force. From his frame to keep a water particle in circular motion a force towards the center is needed. In the rotating drum of washing machine there is not enough force towards the center on the water particle to keep it in circular motion. So from the Newton's First Law of Motion the inertial force expels the water particles away from the drum.          

Q#3

A small coin is put on the record rotating at 33⅓ rev/minute. The coin does not slip on the record. Where does it gets the required centripetal force from ?

Answer:   
The required centripetal force is the force of friction.    

Q#4
A bird while flying takes a left turn. Where does it get the the required centripetal force from?

Answer:   
When a bird takes left or right turn it does not remain horizontal but tilts like a plane. Thus pressing the air with greater area of the underside. As per Newton's Third Law of Motion the air underneath also exerts equal and opposite force on the bird, like normal force on a banked circular road. The horizontal component of this force is the required centripetal force for the bird.    

Q#5

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

Answer:   
No, but all angles should be in the same unit.      

Q#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 hands vigorously to remove the water as much as you can. Why is water removed in this process?

Answer: 
Shaking the hand gives acceleration to he of hand and to remain the water particles attached to hand require a resultant force in the direction of acceleration. The force of the adhesion between the water particles and the hand is not sufficient to transfer the force applied by hand to the particle. So, due to inertial force water is removed. 

Q#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 (Figure 7-Q1). Which wall (inner or outer) will exert a nonzero normal contact force on the block?

Answer:
Since the uniform circular motion has a centripetal acceleration and there must be a resultant nonzero force in the direction of acceleration ie a centripetal force. In this case the outer wall will exert a nonzero normal force on the block in the direction of center of the tube.

Q#8
Consider the circular motion of 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.

Answer: (b)        

Q#9
A car driver going at some speed  v suddenly finds a wide wall at distance r. Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?

Answer: 
To suggest the right action, the values of v, r and coefficient of friction between the road and the tyres of the car must be known. Since the wall is found suddenly it is better to turn the car in a circle of radius r as well as apply the brakes simultaneously to avoid hitting the wall.         

 Q#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.  

Answer:
When the heavy mass is hanging from a string and is in equilibrium without breaking it, the weight of mass is balanced by tension in the string. But when the same mass is set into oscillation it moves on an arc of a circle having radius equal to length of the string ie it has a circular motion. Due to the circular motion the mass has a centripetal acceleration and to maintain this acceleration the string applies a centripetal force on the mass in addition to the tension in equilibrium position. Thus, the tension in the string increases due to the oscillation and it breaks.

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