Two identical blocks A and B, each of mass 'm' resting on smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is

The correct option is A

After triking with A, the block C comes to rest and now both block A and B moves with velocity V, when compression in spring is maximum.
By the law of conservation of linear momentum
$mv=(m+m)V\Rightarrow V=\frac{v}{2}$
By the law of conservation of energy
K.E. of block C = K.E. of system + P.E. of system
$\frac{1}{2}m{v}^2=\frac{1}{2}\left(2m\right)V^2+\frac{1}{2}k{x}^2$
$\Rightarrow \frac{1}{2}m{v}^2=\frac{1}{2}\left(2m\right)(\frac{v}{2}{)}^2+\frac{1}{2}k{x}^2$
$\Rightarrow k{x}^2=\frac{1}{2}m{v}^2$
$\Rightarrow x=v\sqrt{\frac{m}{2k}}$