Wedge is fixed on horizontal surface. Block `A` is pulled upward by applying a force `F` as shown in figure and there is no friction between the wedge and the block `A` while coefficient of friction between `A` and `B` is `mu`. If there is no relative motion between the block `A` and `B` then frictional force developed between `A` and `B` is

Options

A. `[(F+(m-M)g sin theta)/((m+M))]m cos theta`
B. `mumg`
C. `[(F-(m+M)gsintheta)/((m+M))]mcostheta`
D. `mumg//2`

Answer

C

Explanation

`a` is acceleration along up the incline
`F-(M+m)g sin theta=(M+m)a`……(i)
`f=ma cos theta`…..(ii) solving equation -(i) and (ii)
`f=[(F-(M+m)g sin theta)/(M+m)]m cos theta`