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. `mu` mg
C. `[(F - (m +M) g sin theta)/((m + M))] m cos theta `
D. `mu` mg / 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 eqns. (i) and (ii)
`f = [(F - (M + m )"g sin" theta)/(M + m)] "m cos" theta`