A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle `theta` to the vertical. The minimum value of coefficient of friction of friction between the block and the surface for which the block will remain in equilibrium is

Options

A. `(P+Q sin theta)/(mg+Qcos theta)`
B. `(P cos theta+Q)/(mg-Q sin theta)`
C. `(P+Q cos theta)/(mg+Q sin theta)`
D. `(Psin theta+Q)/(mg-Q cos theta)`

Answer

A

Explanation

`Q cos theta+mg=N`
`P+Q sin theta=muN`
`therefore mu=(P+Qsin theta)/(Q cos theta+mg)`