Answers to Problems on (Newton's Laws of Motion) HC Verma's Questions for Short Answer (1-8)

 Q#1

The apparent weight of an object increases in an elevator while accelerating upward. A moongfaliwala sells his moongfali using a beam balance in an elevator. Will he gain more if the elevator is accelerating up?

Answer:
A beam balance compares the weight of an object put at one side with respect to the standard weight put at the other side. So while the elevator is going up, weights on both sides of the balance will gain equally. The moongfaliwala thus would not gain more.

Q#2
A boy puts a heavy box of mass M on his head and jumps down from the top of a multi-storied building to the ground. How much is the force exerted by the box on his head during his free fall? Does the force greatly increase during the period he balances himself after striking the ground?
Answer: During his free fall the box does not exert any force on the head of the boy. It can be explained by taking the frame of reference in the boy. Since the boy is accelerating downward with "g" acceleration, this frame will be a non-inertial frame. To apply Newton's law in a non-inertial frame we add a pseudo force(-ma) to the system along with the other forces acting on it, where a is the acceleration of the frame. In this case a = g.

Consider the box as a system. The forces on it are gravity force weight of the box Mg downward, and the pseudo force upward (-Mg). Adding these forces we get zero. So no force is applied by the box on the boy.

Now consider the period when he balances himself after striking the ground. The feet of the boy has come to rest and he tries to bring the box (that has gained velocity) to rest by pushing it up. So he applies a great force upward to decelerate it. And according to Newton's third law of motion, the box also applies equal and opposite force on the boy.

Q#3
A person drops a coin. Describe the path of the coin as seen by the person if he is in (a) a car moving at a constant velocity and (b) in a free-falling elevator.

Answer:
(a) A car moving with a constant velocity is an inertial frame of reference. So the person will see the dropped coin falling to the floor in a straight line.

(b) A free falling elevator is a non-inertial frame of reference because it is accelerating towards the ground with g. So along with the force on the coin, its weight 'mg', we shall add a pseudo force '-mg' to it, where m is the mass of the coin. It results in zero force or no force on the coin. So the person in the free-falling elevator will see no movement in the coin. It will remain stable to the point where he dropped it.

Q#4
Is it possible for a particle to describe a curved path if no force acts on it? Does your answer depend on the frame of reference chosen to view the particle? 

Answer:
The answer actually depends upon the frame of reference chosen. If it is an inertial frame then with no force there will not be a curved path for the particle. But if the frame of reference chosen is non-inertial, a pseudo force -ma will have to be applied to the particle where m is mass of the particle and a is the acceleration of the non-inertial frame. It will give the particle a pseudo acceleration ( –a) as viewed from this frame. If the particle was moving with a uniform velocity in a line with some angle to the direction of 'a' with no force in the inertial frame, the path of the particle will appear curved if viewed from the non-inertial frame with acceleration a.

Q#5  
You are riding a car. The driver suddenly applies the brakes and you are pushed forward. Who pushed you forward.

Answer:
When riding a car our body also moves with the velocity of the car and it does not want to change its state of uniform velocity due to inertia, as Newton's first law says. When the driver suddenly applies brakes the lower part of our body in contact with the car's seat come to rest with the car (due to friction) while the upper part moves forward in inertia. So due to the inertia of our body, our body is pushed forward.

Q#6
It is sometimes heard that the inertial frame of reference is only an ideal concept and no such inertial frame actually exists.

Answer:
In an inertial frame, acceleration a of a particle is zero if and only if Net force F on the particle is zero. For example, a book kept on a table has a=0 and sum of all forces on the book is zero, so we call earth an inertial frame but if accurately measured the sum of all forces on the book would not be zero. It will be very close to zero, so for all practical purposes we take the earth as an inertial frame but it is an ideal concept and no such inertial frame exist.

Q#7
An object is placed far away from all the objects that can exert force on it. A frame of reference is constructed by taking the origin and axes fixed in this object. Will the frame be necessarily inertial?

Answer:
Since the origin and the axes are fixed in the object, the frame of reference will always move with it. The acceleration of the object with reference to this frame will always be zero. Now the sum of forces on the object will also be zero because no other object can exert force on it. So in this frame of reference always a = 0 for F = 0. So it is an inertial frame.

Q#8

Figure (5-Q1) shows a light spring balance connected to two blocks of mass 20 kg each. The graduations in the balance measure the tension in the spring. (a) what is the reading of the balance? (b) will the reading change if the balance is heavy, say 2.0 kg? (c) what will happen if the spring is light but the blocks are unequal masses?

Answer:
(a) The reading in the balance is 20 kg.

(b) Yes, if the balance is heavy the reading will change because the tension in the string will change.

(c) When the blocks are of unequal masses, there will be a net force on the system and it will start to move if the pulleys are frictionless. The tension in the string will change and so will be the reading of the balance.