In figure, a block `A` of mass `2kg` is moving to the right with a speed `5m//s` on a horizontal frictionless surface. Another block `B` of mass `3kg` a massless spring of spring constant `222N//m` attached to it, is moving to the left on the same surface and with a speed `2m//s` . Let us take the direction to the right as the positive `X-` direction. At some instant, block `A` collides with the spring attached to block `B`. At some other instant , the spring has maximum compression and then, finally, blocks move with their final velocities. Assuming that `(i)` the spring force is conservative and so there is no conversion of kinetic energy to internal energy and `(ii)`, no sound is made when block `A` hits the spring, answer the following questions.

STATEMENT `-1:` The net momentum of a system of two moving particles is zero. Then a particular instant of time, the net angular momentum of system of given two particle is same about any point.
STATEMENT `-2:`If net momentum of a system of two moving particle is zero, then angular mometum of system of given two particles is zero about any point.

Options

A. Statement `-1` is True, Statement `-2` is True, Statement`-2` is a correct explanation for Statement`-1`
B. Statement`-1` is True, Statement`-2` is True, Statement `-2` is NOT a correct explanation for Statement `-1`
C. Statement `-1` is True, Statement`-2` is False
D. Statement `-1` is False, Statement `-2` is True.

Answer

C

Explanation

`vec(L)=vec(r)_(1)xxvec(p)_(1)+vec(r)_(2)xxvec(p)_(2):' vec(p)_(1)+vec(p)_(2)=0`
`=vec(r)_(1)xx(-vec(p)_(2))+r_(2)xxvec(p)_(2)`
`=(vec(r)_(2)-vec(r)_(1))xxvec(p)_(2)`
`vec(L)=vec(r)_(rel)xxvec(p)_(2). `Hence Statement `-1` is True, Statement`-2` is False.
`vec(L)=vec(r)_(rel)xxvec(p)_(2)`