Question

Which of the following statements is not true?
A. The same force of same time causes the same change in momentum for different bodies.
B. The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
C. A greater opposing force is needed to stop a heavy body than a light body in the same times, if they are moving with the same speed.
D. The greater the change in momentum in a given time, the lesser is the force that needs to be applied.

Answer 1

In order to solve this question, we need to use the relation that the rate of change of momentum of a body is equal to the force applied on that body. By studying each given option for this condition, we can find out the wrong statement.

Formula used:
The force applied on a body and the change in momentum of that body are related to each other by the following expression:
$F = \dfrac{{dp}}{{dt}}$

Complete step-by-step answer:
Let us study all the given statements one by one.
A. The same force of same time causes the same change in momentum for different bodies.
This statement is correct because when a force is applied on a body then it produces a change in momentum of that body, so the same force applied for the same duration of time will produce the same change in momentum of that body.
B. The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
This statement is also true as evident from the following relation.
$F = \dfrac{{dp}}{{dt}}$
The change in momentum is also in the same direction as the force.
C. A greater opposing force is needed to stop a heavy body than a light body in the same times, if they are moving with the same speed.
Out of a heavy body and a light body moving with same speed, the heavier body will have greater momentum, so, the heavier body requires a greater opposing force to stop than a lighter body. So, this statement is also true.
D. The greater the change in momentum in a given time, the lesser is the force that needs to be applied.
Since the force and change in momentum are directly proportional to each other, so in order to produce a large change in momentum in a given time, a large force will be required. Therefore, this statement is wrong.
Hence, the correct answer is option D.

So, the correct answer is “Option D”.

Note: It should be noted that the momentum of a body is equal to the product of its mass and its velocity. So, the greater the mass of a body and greater the velocity of a body, greater is its momentum and hence, a greater force will be required to stop such a body.