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

Friction ` = m (mg + Q cos theta)`. Horizontal force ` = P + Q sin theta`. For equilibrium these two are equal. SO `mu = (P + Q sin theta)/(mg + Q cos theta)`