Question

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move?

• A. 20 N
• B. 10N
• C. 12N
• D. 15N

Answer 1

Answer: (A)

Free body diagram (FBD) of the block (shown by a dot) is shown in figure

For vertical equilibrium of the block
$N=mg+F\sin 60^{\circ }$
$=\sqrt{3}g+\sqrt{3}\frac{F}{2}...(i)$
For no motion, force of friction
$f\ge \cos 60^{\circ }$ or $\mu N\ge F\cos 60^{\circ }$
or $\frac{1}{2\sqrt{3}}\left(\sqrt{3}g+\frac{\sqrt{3}F}{2}\right)\ge \frac{F}{2}$
or $g\ge \frac{F}{2}$
or $F\le 2g$ or $20N$
Therefore, maximum value of $F$ is $20N$.