In figure, the stiffness of the spring is `k` and mass of the block is `m`. The pulley is fixed. Initially, the block `m` is held such that the elongation in the spring is zero and then released from rest. Find:
a. the maximum elongation in the spring.
b. the maximum speed of the block `m`. Neglect the mass of the spring and that of the string. Also neglect the friction.

Options

A. `(mg)/(3k)`
B. `(mg)/(k)`
C. `(mg)/(2k)`
D. `(2mg)/(k)`

Answer

D

Explanation

Loss in potential energy `=`gain in energy of spring
`mgx=(1)/(2)kx^2`
`x=(2mg)/(k)`