A spring having a spring constant `k` is fixed to a vertical wall as shown in Fig. A block of mass `m` moves with velocity `v` torards the spring from a parallel wall opposite to this wall. The mass hits the free end of the spring compressing it and is decelerated by the spring force and comes to rest and then turns the spring is decelerated by the spring force and comes to rest and then turns back till the spring acquires its natural length and contact with the spring is broken. In this process, it regains its angular speed in the opposite direction and makes a perfect elastice collision on the opposite left wall and starts moving with same speed as before towards right. The above processes are repeated and there is periodic oscillation.
Q. What is the maximum compression produced in the spring?

Options

A. (a)`vsqrt((m)/(k))`
B. (b)`sqrt((m)/(k))`
C. (c)`vsqrt(mk)`
D. (d)`vsqrt((k)/(m))`

Answer

A

Explanation

Using conservation of mechanical energy
`(1)/(2)mv^2=(1)/(2)kx^2impliesx^2=(m)/(k)impliesx=vsqrt((m)/(k))`