An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Options

A. `(Mg)/(K)`
B. `(Mg)/(2K)`
C. `(4Mg)/(K)`
D. `(2Mg)/(K)`

Answer

D

Explanation

The block will perform a vertical S.H.M. When it is in the extreme low position, the extension in the spring is maximum.
Let it be x.
Then the work done by the weight of the block
= P.E. stored in the spring
`therefore Mgx=(1)/(2) Kx^(2) therefore x=(2 Mg)/(K)`