A block of mass `m` attached in the lower and vertical spring The spring is hung from a calling and force constant value `k` The mass is released from rest with the spring initially unstreched The maximum value of extension produced in the length of the spring will be

Options

A. `Mg/k`
B. `2 Mg/k`
C. `4 Mg/k`
D. `Mg/2k`

Answer

`(2)`

Explanation

When the mass attached to a spring fixed at the other end is allowed to fall suddenly, it extends the spring by x. Potential energy lost by the mass is gained by the spring.
`Mgx = 1/2 kx^(2) Rightarrow x = (2Mg)/(k)`