Question

In the figure, block $m_1$ is loaded on block $m_2$. If there is no relative sliding between the blocks and the inclined plane is smooth, the frictional force acting between the blocks is:

• A. $\mu m_2\sin \theta$
• B. $\mu m_1\cos \theta$
• C. $\mu m_1\sin \theta$
• D. Zero

Answer 1

The correct option is D Zero

Assuming no friction between the surfaces, acceleration of
block $1$ is


Since, the blocks can only move along the inclined plane, so all forces $\perp$ to inclined plane will be balanced for respective blocks.

Acceleration of both blocks down the inclined plane is:

$a_1=\frac{\text{Net Force}}{\text{mass}}=\frac{m_{1}g\sin \theta }{m_1}=g\sin \theta$

Acceleration of block $2$

$a_2=\frac{\text{Net Force}}{\text{mass}}=\frac{m_{2}g\sin \theta }{m_2}=g\sin \theta$

$\Rightarrow$ relative acceleration between blocks 1 and 2 is:
$(a_1-a_2)=(g\sin \theta -g\sin \theta )=0$

Hence, we can say that there is no tendency of slipping between blocks, as both will move with same acceleration down the incline.
$\therefore$frictional force $f=0$ between block$1$ and block$2$.