A small block of mass m is fixed at upper end of a massive vertical spring of spring constant `k=(2mg)/(L)` and natural length `10L` The lower end of spring is free and is at a height L from fixed horizontal floor as shown. The spring is initially unstressed and the spring block system is released from rest in the shown position.
Q. As the block is coming down, the maximum speed attained by the block is

Options

A. `sqrt(gL)`
B. `sqrt(3gL)`
C. `(3)/(2)sqrt(gL)`
D. `sqrt((3)/(2)gL)`

Answer

C

Explanation

At the instant block is in equilibrium position its speed is maximum and compression in spring is x given by
`kx=mg` (i)
From conservation energy,
`mg(L+x)=(1)/(2)kx^2+(1)/(2)mv_(max)^2` .(ii) From Eqs (i) and (ii) we get `v_(max)=(3)/(2)sqrt(gL)`