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 $g\left(\frac{1+\mu }{1-\mu }\right)$

$N\sin \theta +\mu N\cos \theta =ma$
$N\cos \theta -\mu N\sin \theta =mg$
Putting $\theta ={45}^{\circ }$ and solving these two equations we get,
$a=g\left(\frac{1+\mu }{1-\mu }\right)$