A block of mass m starts at rest at height h on a frictionless inclined plane. The block slides down the plane, travels across a rough horizontal surface with coefficient of kinetic friction `mu_(1)` and compresses a spring with force constant k a distance x before momentarily 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 expression for the maximum height h' that the block reaches on its return is :
.

Options

A. `mgh'=mgh-mu mg d`
B. `mgh' = mgh+mu mgd`
C. `mgh'= mgh+mu mgd+kx^(2)`
D. `mgh'=mgh-mu mgd - kx^(2)`

Answer

A

Explanation

A block of ………….
Final `P.E` of block = Initial `P.E.` of block + work done by friction
`:.` mgh' = mgh - mu mgd