Question

Rate of change of linear momentum is equal to:
(A) Mass/Acceleration
(B) Acceleration
(C) Mass
(D) Mass x Acceleration

Answer 1

Hint: According to newton’s second law, “the rate of change of momentum is proportional to the net force acting on a system”. This statement was later modified to “the rate of change of momentum is equal to the net force acting on a system”.

Complete step by step solution:
Linear Momentum is defined as the product of mass and velocity.
Rate of change of any quantity is taken to be with respect to time whenever not mentioned.
Hence rate of change of linear momentum can be written as $\dfrac{{dP}}{{dt}}$, where P denotes linear momentum and t denotes time.
 Since Linear momentum can be written as $P = mv$ .
Rate of change of linear momentum = $\dfrac{{d(mv)}}{{dt}}$.
If mass of the system is assumed to be constant
Rate of change of linear momentum = $m\dfrac{{d(v)}}{{dt}}$.
$\dfrac{{d(v)}}{{dt}}$ represents rate of change of velocity, which is equal to acceleration, say a.
We can now write
Rate of change of linear momentum = $ma$.
Hence, Rate of change of linear momentum = mass x acceleration

Therefore, the correct answer to the question is option : D.

Note: In this question, we have assumed the mass of the system to be constant. Mostly when we talk about any body or particle in a question, its mass doesn’t change. The mass of a body can change if mass is leaking the system or mass is being added to the system. It can also change if mass is getting converted to energy through Einstein’s famous equation.