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

Answer

A

Explanation

(a) `N=mg-Q cos theta`

`P+Q sin theta =mu N=mu(mg-Q cos theta)`
`therefore" " mu =(P+Q sin theta)/(mg+Q cos theta)`