A block of mass `m` lying on a horizontal plane , is acted upon by a horizontal force p and another force `Q` inclined at an angle `theta` to the vertical .The block will remain in equilibrium if the coefficient of friction between it and the surface is (assume `p gt Q)`

Options

A. `(P+Qsintheta)//(mg+Qcostheta)`
B. `(Pcostheta+Q)//(mg-Qsintheta)`
C. `(P+Qcostheta)//(mg+Qsintheta)`
D. `(P sintheta-Q)-(mg-Qcostheta)`

Answer

A

Explanation

Friction force `=mmuR=mu(mg+Qcostheta)`
And horizontal push `=P+Qsintheta`
For equilibrium, we have
`mu(mg+Qcostheta)=P+Qsintheta`
`mu=(P+Qsintheta)/(mg+Qcostheta)`