If the coefficient of friction between `A` and `B` is `mu`, the maximum acceleration of the wedge `A` for which `B` will remain at rest with respect to the wedge is

Options

A. `mug`
B. `g((1+mu)/(1-mu))`
C. `(g)/(mu)`
D. `g((1-mu)/(1+mu))`

Answer

B, C, D

Explanation

FBD of block B w.r.t. wedge A, for maximum `a`:
Perpendicular to wedge:
`sumf_y^`=(mgcostheta+masintheta-N)=0`
and `sumf_x^`=mgsintheta+muN-macostheta=0` (for maximum a)
`impliesmgsintheta+mu(mgcostheta+masintheta)-mcostheta=0`
`implies a((gsintheta+mugcostheta))/(costheta-musintheta)`
For `theta=45^@`
`a=((tan45^@+mu)/(cot45^@-mu))`,`a=g((1+mu)/(1-mu))`