Question

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

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

Answer 1

Answer: (B)

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

From the free body diagram

$\sum F=0$

$2+mg\sin 30=\mu mg\cos {30}^o$.............................$\left(i\right)$

$10=mg\sin 30+\mu mg\cos {30}^o$.....................$\left(ii\right)$

Adding eq $\left(i\right)$ and $\left(ii\right)$, we get

$12=2\mu mg\cos 30$

$6=\mu mg\cos 30$.......................................$\left(iii\right)$

$4=mg\sin 30$.............................................$\left(iv\right)$

From eqn $\left(iii\right)$ and $\left(iv\right)$, we get

$\frac{3}{2}=\mu \times cot{30}^0$

$\frac{3}{2}=\mu \times \sqrt{3}$
$\mu =\frac{\sqrt{3}}{2}$