Question

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

• A. $15N$
• B. $5N$
• C. $10N$
• D. $20N$

Answer 1

Answer: (D)

The forces acting on the block are shown. Since the block is not moving forward for the maximum force $F$ applied, therefore
$F\cos 60^{\circ }=f=\mu N\dots$ (i)
(Horizontal Direction) and
$F\sin 60^{\circ }+mg=N$.....(ii)
From (i) and (ii)

$F\cos 60^{\circ }=\mu F\sin 60^{\circ }+mg$
$\Rightarrow F=\frac{\mu mg}{\cos 60^{\circ }-\mu \sin 60^{\circ }}$
$=\frac{\frac{1}{2\sqrt{3}}\times \sqrt{3}\times 10}{\frac{1}{2}-\frac{1}{2\sqrt{3}}\times \frac{\sqrt{3}}{2}}=\frac{5}{\frac{1}{4}}=20N$