Consider the following two statements.
a. Linear momentum of a system of particles is zero.
b. Kinetic energy of a system of particles is zero. Then

Options

A. a implies b and b implies a.
B. a does not imply b and b does not imply a
C. a implies b but b does not imply a
D. a does not imply b but b implies a

Answer

d

Explanation

Here, `E_k=1/2mv^2`
As `E_k=0 v=0` `(because m ne 0)`
Also, momentum= mv
It v=0 , momentum = 0
Thus (b) implies (a).
But, when there is no resultant momentum, there can never be a net force by second law.This can result in a constant non-zero velocity an hence K.E. Thus (a) does not imply (b).