Question

STATEMENT A- Linear momentum of a system of particles is zero.
STATEMENT B- Kinetic energy of system of particles is zero.

• A. A does not imply B and B does not imply A.
• B. A implies B but B does not imply A
• C. A does not imply B but B implies A
• D. A implies B and B implies A.

Answer 1

The correct option is C A does not imply B but B implies A

Consider a system consisting of masses $m_1,m_2$ having velocities $v_1,v_2$
Net momentum $=m_1{v}_1+m_2{v}_2$
Net kinetic energy $=\left(\frac{1}{2}\right)m_1{v}_1^2+\left(\frac{1}{2}\right)m_2{v}_2^2$

Case $\left(i\right)$
Let $v_1=v,v_2=-v$ and $m_1=m_2=m$
Then net momentum = 0 but net kinetic energy is not equal to zero.
A does not imply B

Case $\left(ii\right)$
If $v_1=v_2=0,$ Net Kinetic energy is zero.
Also net momentum is zero.
Hence B implies A.
Hence (c) is correct