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 acceleration of the prism is g cos `theta`
B. the acceleration of the prism is g tan `theta`
C. the minimum coefficient of friction between the block and prism is`mu_(min)= tan theta`
D. the minimum coefficient of friction between block and prism is `mu_(min)= tan theta`

Explanation

Both blocks have acceleration g sin `theta`

(In frame of `m_(1))`
N `=m_(2)g -m_(2)g sin^(2) theta=m_(2) gcoc^(2) theta`
f `=muN`
`rArrf=mum_(2)gcos ^(2)theta` ...(1)
`=m_(2)g sin theta . costheta` ...(2)
comparing `equ^(n) (1)&(2)`
`mum_(2) gcos ^(2)theta =m_(2)g sintheta cos theta`
`mu cos theta = sin theta`
`tan theta = mu`