A block is placed on a rough prism. The block will be stationary relative to prism if acceleration of prism $a$ is:

$(a, c)$ Minimum value of $a$:– For this the sliding tendency is down the plane and friction acts up the plane:

        $N = mg \cos \alpha +m{a}_{min}\sin \alpha$

and $mg \sin \alpha = \mu N+m{a}_{min} \cos \alpha$

After solving above equations, we get

$a_{min}= \frac{g\left(1-\mu cot\alpha \right)}{\left(\mu +cot\alpha \right)}$