A triangular prism of mass M with a block of mass m placed on it is released from rest on a smooth inclined plane of inclination $θ$ . The block does not slip on the prism. Then

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the minimum coefficient of friction between the block and the prism is $µ_{m i n} = c o t θ$

the minimum coefficient of friction between the block and the prism is $µ_{m i n} = \tan θ$

the acceleration of the prism is g cosθ

the acceleration of the prism is g sinθ

answer is B, D.

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Detailed Solution

As the block does not slip on prism, the combined acceleration of the prism is $a = g \sin θ$ .

mg $\sin θ$ is the pseudo force on m.

$N + m g \sin θ \sin θ = m g$

Or $N = m g \cos^{2} θ$

and for no slipping ,

so $m g \sin θ \cos θ \leq μ N$

$m g \sin θ \cos θ \leq μ m g \cos^{2} θ$ or $μ \geq \tan θ$

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