A spring is loaded with two blocks `m_(1)` and `m_(2)` where `m_(1)` is rigidly fixed with the spring and `m_(2)` is just kept on the block `m_(1)`. The maximum energy of oscillation is possible for the system having the block `m_(2)` in constant with `m_(1)` is

Options

A. `(m_(1)^(2)g^(2))/(2K)`
B. `(m_(2)^(2)g^(2))/(2K)`
C. `((m_(1)+m_(2))^(2)g^(2))/(2K)`
D. `((m_(1)+m_(2))g)/(2K)`

Answer

C

Explanation

`m_(2)g -N = m_(2)a = m_(2) omega^(2)A`

`A = (g//omega^(2))` for loosing contact `omega^(2) = (k)/(m_(1)+m_(2))`
`U_(max) = (1)/(2)kA^(2) = ((m_(1)+m_(2))^(2)g^(2))/(2k)`