Question

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2 \,N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\, N$. The coefficient of static friction between the block and the plane is : [Take $g = 10\, m/s^2$]

• A. $\frac{2}{3}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{\sqrt{3}}{2}$

Answer 2

$2+m g \sin 30=\mu m g \cos 30^{\circ}$
$10=m g \sin 30+\mu m g \cos 30^{\circ}$
$\quad=2 \mu m g \cos 30-2$
$6=\mu m g \cos 30$
$4=m g \sin 30$
$\frac{3}{2}=\mu \times \sqrt{3}$
$\mu=\frac{\sqrt{3}}{2}$