A small block of mass m os takes slowly up a fixed hemisphere from `P` to `Q` and then slowly down along its surface from `Q` to `S` by force `F`, which at each point of the surface, is tangential to the surface. If the coefficient of friction is `mu`, then the work performed by the force `F` in taking the block from `P` to `S` along the hemispherical surface of radius `R` is :

Options

A. `2mu mgR`
B. `mu mgR`
C. `pi mu mgR`
D. None of these

Answer

A

Explanation

A small block …………
`W = int mu mg cos theta ds`
`W = overset(2R)underset(0)int mu mgdx`

`W = 2mu mg R`
Work done agasinst gravity is zero.