Question

Which of the following statements are correct regarding linear momentum of a body? (This question has multiple correct options)
A. It is a measure of the quantity of motion contained in a body.
B. change in momentum is the measurement of impulse.
C. Impulse and acceleration act in the same direction to the change in momentum.
D. In case of uniform circular motion, the linear momentum is conserved.

Answer 1

Hint: Linear momentum is defined mathematically as the product of the mass of a body and the velocity with which the body moves. It can be defined using different ways. We will look at the options provided one by one and decide if the given option will be correct or not.

Formula used:
$\vec{I}=\int{\vec{F}.dt}$
\[\vec{F}=\dfrac{d\vec{P}}{dt}\]

Complete answer:
For the first option we have, it is a measure of quantity of motion contained in a body. Momentum does tell us how much force over an interval of time will be needed to bring the body to a complete stop. So, it can be defined as a measure of the quantity of motion contained in a body. Hence, this option will be correct.

The second question says that the change in momentum is the measurement of impulse. Impulse is defined as the product of force and time for which the force is applied. Mathematically, $\vec{I}=\int{\vec{F}.dt}$and Newton’s second law of motion defines force as the rate of change of momentum. So
\[\vec{F}=\dfrac{d\vec{P}}{dt}\Rightarrow d\vec{P}=\vec{F}.dt\Rightarrow \Delta \vec{P}=\int{\vec{F}.dt}\]

As we can see the change of momentum is equal to the impulse. Hence, this option is also correct.
As was derived previously, the change in momentum and the force are vectors in the same direction. The acceleration will also act in the same direction as the force. So, all three will be in the same direction. Hence, this option is also correct.

The last option says that in case of uniform circular motion, the linear momentum is conserved. During uniform circular motion, the direction of motion changes constantly. As the direction of velocity changes constantly and the direction of momentum is the same as that of velocity, the direction of linear momentum will keep on changing and won’t be conserved.

So, the correct answer is “Option A,B and C”.

Note:
The definition of momentum as the product of mass and velocity is only valid for objects moving at low velocity. At relativistic speeds, the value of momentum is given by mass-energy relation given by Einstein. Only the value of momentum changes but other properties remain the same.