Question

A block of mass $m$ is pressed against a vertical wall by applying a force $P$ at an angle $\theta$ to the horizontal as shown in the figure. As a result, if that block is prevented from falling down and $\mu$ is the coefficient of static friction between the block and the wall, the value of P $=$

• A. $\frac{mg}{\mu sin\theta -cos\theta }$
• B. $\frac{mg}{\mu sin\theta +cos\theta }$
• C. $\frac{mg}{\mu cos\theta -sin\theta }$
• D. $\frac{mg}{\mu cos\theta +sin\theta }$

Answer 1

The correct option is C $\frac{mg}{\mu cos\theta -sin\theta }$

From the FBD of block, we have
$Pcos\theta =N$ where $N$ is normal reaction.
$\mu N-Psin\theta =mg$
$\mu Pcos\theta -Psin\theta =mg$
$P=\frac{mg}{\mu cos\theta -sin\theta }$