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

• A. $\frac{P+Q \sin \theta}{m g+Q \cos \theta}$
• B. $\frac{P \cos \theta+Q}{m g-Q \sin \theta}$
• C. $\frac{P+Q \cos \theta}{m g+Q \sin \theta}$
• D. $\frac{P \sin \theta-Q}{m g-Q \cos \theta}$

Answer 1

Answer: (A)

For equilibrium of the block
$N =m n g+Q \cos \theta $
$Q \sin \theta+P =\mu N $
$Q \sin \theta+P =\mu(m g+Q \cos \theta)$

$\therefore \mu=\left(\frac{Q \sin \theta+P}{m g+Q \cos \theta}\right)$