Question

What is the maximum value of the force $\text{F}$ such that the block shown in the arrangement, does not move ? (Take $g=10{\text{m/s}}^2$)

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

Answer 1

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

Here by free body diagram of the block with resolved forces,

For body to be in equilibrium by balancing forces, we get
$N=(Mg+F\sin {60}^{\circ })$
$F\cos {60}^{\circ }=f$

For limiting case $f=\mu N$
$f=F\cos {60}^{\circ }=\mu N=\mu (Mg+F\sin {60}^{\circ })\Rightarrow F=\frac{\mu Mg}{\cos {60}^{\circ }-\mu \sin {60}^{\circ }}=\frac{\frac{1}{2\sqrt{3}}\times \sqrt{3}\times 10}{\frac{1}{2}-\frac{1}{2\sqrt{3}}\times \frac{\sqrt{3}}{2}}$

Hence the maximum force $F_{\text{max}}=20\text{N}$

Option A is the correct answer.