All surfaces are smooth in following figure. Find F such that block remains stationary with respect to wedge.

Options

A. `(M+m)g tan beta`
B. `g tan beta`
C. `mg cos beta`
D. `(M+m)g cosec beta`

Answer

A

Explanation

Acceleration of the system:
`a=(P)/(M+m)`…(i)
The FBD of mass m is shown in the fig.
`R sin beta=ma` …(ii)
`R cos beta=mg`…(iii)
`a=g tan beta`
Putting value of a in (i), we get
`P=(M+m)g tan beta`.