Question

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:

• A. $\mu g$
• B. $g\left(\frac{1+\mu }{1-\mu }\right)$
• C. $g\left(\frac{1-\mu }{1+\mu }\right)$
• D. $\frac{g}{\mu }$

Answer 1

The correct option is B $g\left(\frac{1+\mu }{1-\mu }\right)$

For maximum acceleration the block is just about to move up the incline

$ma\cos \theta =mg\sin \theta +f_l$
$f_l=\mu N$
$N=mg\cos \theta +ma\sin \theta$
$\Rightarrow ma\cos \theta =mg\sin \theta +\mu (mg\cos \theta +ma\sin \theta )$
$\Rightarrow a=\frac{g(\sin \theta +\mu \cos \theta )}{(\cos \theta -\mu \sin \theta )}$
$\sin \theta ={45}^{\circ }\Rightarrow \sin \theta =\cos \theta =\frac{1}{\sqrt{2}}$
$\Rightarrow a=\frac{g(1+\mu )}{(1-\mu )}$