Question

Two block $A$ and $B$ of equal mass $3\text{kg}$ each are connected over a massless pulley as shown in figure. The block $A$ is placed on a rough inclined plane of angle ${30}^{\circ }$. The coefficient of friction between block $A$ and inclined plane is $0.6$. The friction force acting on the block $A$ is
(Assume $g=10{\text{ms}}^{-2}$ )

• A. Zero
• B. $15.6\text{N}$
• C. $18\text{N}$
• D. $15\text{N}$

Answer 1

The correct option is D $15\text{N}$


$m_{B}g=30\text{N}$
$m_{A}g\sin \theta =30\times \frac{1}{2}=15\text{N}$
Net pulling force $=30-15=15\text{N}$
$f_1=\mu m_{A}g\cos \theta$
$=0.6\times 30\times \frac{\sqrt{3}}{2}$
$=9\sqrt{3}=9\times 1.732=15.6\text{N}$
$\because f_1>$ pulling force
$\therefore f=$ pulling force $=15\text{N}$
$\therefore$ (d)