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

Options

A. The accelaration of the prism is `g cos theta`
B. The accelaration of the prism is `g tan theta`
C. The minimum coefficient of friction between the block the block and the prism is `mu _(min) = cot theta`
D. The minimum coefficient of friction between the block the block and the prism is `mu _(min) = tan theta`

Answer

d

Explanation

As the block does not slip on prism the combined acceleration of the prism is
`a = g sin theta`
`mg sin theta` is the psendo on m
`N +mg sin theta sin theta = mg`
`N = mg cos^(2) theta`
And for no slipping , `mg sin theta cos theta le mu N`
`mg sin theta cos theta le mu mg cos^(2) theta or mu ge tan theta`