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 the figure.


For vertical equilibrium of the block,

$N=mg+F\sin {60}^{\circ }$

$N=\sqrt{3}g+F\frac{\sqrt{3}}{2}.........\left(1\right)$

For no motion, force of friction,

$f\ge F\cos {60}^{\circ }\Rightarrow \mu N\ge F\cos {60}^{\circ }$

$\frac{1}{2\sqrt{3}}(\sqrt{3}g+\frac{\sqrt{3}F}{2})\ge \frac{F}{2}$

$\Rightarrow g\ge \frac{F}{2}$

$F\le 2g=20\text{N}$

Therefore, the maximum value of $F$ is $20\text{N}$.

Hence, option $\left(\text{A}\right)$ is correct.