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. None of these

Explanation

Let the required amplitude be `A`. For this amplitude of oscillation the normal contact force between the blocks can be given as
`m_(2)g-N=m_(2)a`, where `a = omega^(2)A`
`rArr m_(2)g-N=m_(2)omega^(2)A`
Putting `N=0` for just losing contact for maximum amplitude, we obtain
`A=(g)/(omega^(2))`, where `omega=` angular frequency of oscillation of `(m_(1)+m_(2))` and the spring
Putting `omega^(2)=(k)/(m_(1)+m_(2))`, we obtain
`A=((m_(1)+m_(2))g)/(k)`
`:. U_(max)=(1)/(2)kA^(2)=((m_(1)+m_(2))^(2)g^(2))/(2k)`