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

Answer

b

Explanation

Frictional force` = muR = mu (mg + Q cos theta)` and horizontal push `= P - Q sin theta`
For equilibrium we have
`mu (mg + Q cos theta) = P - Q sin theta rArr mu = (P - Q sin theta )/(mg + Q cos theta)`