A block of mass m starts at rest at height on a frictionless inclined plane. The block slides down the plane, travels across a rough horizontal surface with coefficient of kinetic friction `mu` and compresses a spring with force constant `k` a distance `x` before momentarilly coming to rest. Then the spring extends and the block travels back across the rough surface, sliding up the plane. The block travels a total distance d on rough horizontal surface. The correct experssion for the maximum height h' that the block reaches on its return is :

Options

A. `mgh'=mgh-mumgd`
B. `mgh'=mgh+mumgd`
C. `mgh'=mgh+mumgd+kx^(2)`
D. `mgh'=mgh-mumgd-kx^(2)`

Answer

A

Explanation

Final `P.E.` of block `=` Initial `P.E.` of block `+` work done by friction
`:. Mgh' =mgh-mu mg d`