Question

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 upwards. The block will remain in equilibrium, if minimum coefficient of friction between it and the surface is

• A. $\frac{(P+Qsin\theta )}{(mg-Qcos\theta )}$
• B. $\frac{Pcos\theta +Q}{(mg-Qsin\theta )}$
• C. $\frac{P-Qcos\theta }{(mg+Qsin\theta )}$
• D. $\frac{(Psin\theta -Q)}{(mg-Qcos\theta )}$

Answer 1

The correct option is A $\frac{(P+Qsin\theta )}{(mg-Qcos\theta )}$

$N=mg-Qcos\theta$
$P+Qsin\theta =\mu N=\mu (mg-Qcos\theta )$
$\therefore \mu =\frac{P+Qsin\theta }{mg-Qcos\theta }$.