Three springs `A,B` and `C` each of force constant `K`, are connected at `O`. The other ends of `B` and `C` can slide on smooth sliders. A pan is hanging from other end of the spring `A`. When a block of mass `m` is placed into he pan, find the amount of workdone by the gravity on block system after it stops vibrating. The spring `C` does not sag :
.

Options

A. `(3m^(2) g^(2))/(2K)`
B. `(m^(2) g^(2))/(K)`
C. `(2m^(2) g^(2))/(K)`
D. `(m^(2) g^(2))/(2K)`

Answer

C

Explanation

The system will adjust in such a way by sliding the spring `C` remains instretched and spring `A` and `B` remains vertical. Thus, effective force constant is given by
`(1)/(K')=(1)/(K)+(1)/(K),K'=(K)/(2)`