Solutions to Problems on (Newton's Laws of Motion) HC Verma's Concepts of Physics objective-II

 Q#1

A reference frame attached to earth
(a) is an inertial frame by definition
(b) cannot be an inertial frame because the earth is revolving around the sun
(c) is an inertial frame because Newton's laws are applicable in this frame
(d) cannot be an inertial frame because the earth is rotating about its axis. 

Answer: (b), (d).    
(b) and (d) are correct because theoretically earth is not an inertial frame. Due to its revolution around the sun and rotation about its own axis, its velocity changes continuously, means has acceleration. So the earth and any frame attached to it is non-inertial.

Q#2
A particle stays at rest as seen in a frame. We can conclude that
(a) The frame is inertial  
(b) resultant force on the particle is zero
(c) the frame may be inertial but the resultant force on the particle may be zero
(d) the frame may be non inertial but there is a nonzero resultant force. 

Answer: (c), (d).
(a) is incorrect because if the particle and the non-inertial frame both are moving with same acceleration, the particle will be seen at rest from this frame. So we cannot conclude that the frame is inertial.

(b) is  also not correct. Suppose as viewed from an inertial frame a force F produces an acceleration a in a particle. If  this particle be seen from a non-inertial frame that too is moving with same acceleration in the same direction, it will seem to be at rest. But the force on the particle is not zero.
(c) and (d) are possible conditions.  

Q#3
A particle is found to be at rest when seen from a frame S₁and moving with a constant velocity when seen from another frame S₂. Mark out the possible options.
(a) Both the frames are inertial
(b) Both the frames are non-inertial
(c) S₁ is inertial and S₂ is non-inertial
(d) S₁ is non-inertial and S₂ is inertial

Answer: (a), (b).
(a) is possible. Suppose in one inertial frame the particle is at rest. If viewed from another frame which is moving with a constant velocity the same particle will be seen as moving with a constant velocity. but this frame is also inertial.

(b) is also possible. Suppose a non-inertial frame and the particle both are moving with same acceleration in the same direction. From this frame the particle will be seen at rest. If this particle is seen from another non-inertial frame moving with the same acceleration in the same direction but with different velocity at that instant, it will seem to be moving with a constant velocity.
(c) and (d) are not true because this condition is not possible if one frame is inertial and another non-inertial. 

Q#4

Figure (5-Q3) shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region
(a) AB          (b) BC            (c) CD             (d) DE
    
Answer: (a), (c).
Only in the reason AB and CD the displacement is directly proportional to time, it means that the particle is moving with a uniform velocity. So in this reason force on the particle is zero.    

Q#5

Figure (5-Q4) shows a heavy block kept on a friction-less surface and being pulled by two ropes of equal mass m. At t = 0 the force on the left rope is withdrawn but the force on the right rope continues to act. Let F₁and F₂ be the magnitude of the forces by the right rope and the left rope on the block respectively.
(a) F₁ = F₂ = F  for t < 0        
(b) F₁ = F₂ = F + mg for t < 0                
(c) F₁ = F, F₂ = F  for t > 0                      
(d) F₁ < F, F₂ = F  for t > 0

Answer: (a).
(a) is correct because as seen in the figure for t < 0, F₁ = F₂ =F. For the same reason (b) is incorrect.

Since at t = 0 the force on the left rope is withdrawn so at t > 0, F₁ ≠ F, F₂ ≠ F. So (c) is in correct.
Since force on the left rope is withdrawn at t = 0, so at t > 0 force by the right rope on the block will not change ie. F₁ will not be less than F. So (d) is incorrect.    

Q#6
The force exerted by the floor of an elevator on the foot of a person standing there is more than the weight of the person if the elevator is
(a) going up and slowing down        
(b) going up and speeding up                
(c) going down and slowing down                      
(d) going down and speeding up  

Answer: (b), (c).
If we are going to use Newton's laws of motion in a non-inertial frame like accelerating elevator, we have to apply a pseudo force on the object that is opposite in the direction of the acceleration and its magnitude is mass times the magnitude of this acceleration. Only in the cases of option (b) and (c) the acceleration of the elevator has direction upwards. In these cases the direction of the pseudo force will be downwards  which will add to the weight of the person.

Q#7
If the tension in the cable supporting an elevator is equal to the weight of the elevator, s equal
to the weight of the elevator, the elevator may be
(a) going up with increasing speed        
(b) going down with increasing speed                
(c) going up with uniform speed                      
(d) going down with uniform speed   

Answer: (c), (d).
In the cases of  (a) and (b) the elevator is accelerating, so pseudo forces will have to be applied on it to apply the Newton's laws of motion. It will result in either increase or decrease in the apparent weight of the elevator. So the tension in the cable will be either more or less than the weight of the lift.

There are no such pseudo forces in the cases of (c) and (d). So the tension in the cable will be equal to the weight of the elevator.

Q#8
A particle is observed from two frames S₁and S₂ . The frame S₂ moves with respect to S₁ with an acceleration a. Let F₁ and F₂  be the pseudo forces on the particle when seen from S₁ and S₂ respectively. Which of the following is not possible?  
(a) F₁ = 0, F₂ ≠ 0 
(b) F₁ ≠ 0, F₂ = 0
(c) F₁ ≠ 0, F₂ ≠ 0 
(d) F₁ = 0, F₂ = 0   
Answer: (d).
(a), (b) and (c) are possible under different values of accelerations of the frames S₁ and S₂ with respect to another inertial frame. But (d) is not possible because due to difference in accelerations of frames the pseudo forces in both frames cannot be equal.   

Q#9
A person says that he measured the acceleration of a particle to be nonzero while no force was acting on the particle.
(a) He is a liar.
(b) His clock might have run slow 
(c) His meter scale might have been longer than the standard.   
(d) He might have used non-inertial frame.         

Answer: (d).
(d) is true because if a particle with no force acting on it is viewed from a non-inertial frame that is moving with a certain acceleration, then the particle will be seen moving with nonzero acceleration.