A horizontal surface is partly smooth and partly rough. A particle is projected along the smooth part with speed u. After travelong a distance d, to rest. If `mu` is the coefficient of friction between particle and surface, the distance moved over the rough surface is:

Options

A. `mud`
B. `(d)/(mu)`
C. `(u^(2))/(2mug)`
D. `d - (u^(2))/(mug)`

Answer

C

Explanation

`v^(2) == u^(2) + 2 as`
`0^(2) = u^(2) + 2(-mug)s`
`s = (u^(2))/(2mug)`