Question

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

• A. $20\text{N}$
• B. $10\text{N}$
• C. $12\text{N}$
• D. $15\text{N}$

Answer 1

The correct option is A $20\text{N}$

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

For vertical equilibrium of the block,
$\text{N = mg + F sin}{60}^{\circ }=\sqrt{3}g+\sqrt{3}\frac{F}{2}....\left(1\right)$
For body to be in rest, force of limiting friction
$f\ge \text{F cos}{60}^{\circ }$
$\mu N\ge \text{F cos}{60}^{\circ }$
or $\frac{1}{2\sqrt{3}}(\sqrt{3}g+\frac{\sqrt{3}F}{2})\ge \frac{F}{2}$
or $g\ge \frac{F}{2}$
or $F\le 2\text{g or}20\text{N}$
Therefore, maximum value of $F$ is $20\text{N}$.