In Fig. Block $m_{2}$ is located on block $m_{1}$ . If there is no relative sliding between the blocks and the plane is smooth, find the friction force between the blocks.

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Solution

Assuming no friction between the surfaces, acceleration of block (1), $a_{1} = \frac{m_{1} g s i n θ}{m_{1}} = g s i n θ$
and acceleration of block (2),
$a_{2} = \frac{m_{2} g s i n θ}{m_{2}} = g s i n θ$
Value of $|_{1} -_{2} | = | g s i n θ - g s i n θ | = 0$
Here we can say there is no tendency of relative sliding. Hence, no friction is present between (1) and (2).

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