Question

A block of mass '$m$' is placed on a wedge of mass '$M$'. Coefficient of friction between them is $\mu >\cot \theta$. The wedge is given an acceleration to its left. Find the maximum acceleration at which block appears stationary relative to wedge.

• A. $\frac{g(\sin \theta -\mu \cos \theta )}{\cos \theta \sin \theta }$
• B. $\frac{g(\sin \theta +\mu \cos \theta )}{\cos \theta -\mu \sin \theta }$
• C. $\frac{g(\sin \theta +\mu \cos \theta )}{\sin \theta -\mu \cos \theta }$
• D. none

Answer 1

The correct option is B $\frac{g(\sin \theta +\mu \cos \theta )}{\cos \theta -\mu \sin \theta }$

From FBD (shown in figure)
for max acceleration, $ma\cos \theta =f+mg\sin \theta =\mu N+mg\sin \theta$
or, $ma\cos \theta =\mu (mg\cos \theta +ma\sin \theta )+mg\sin \theta$
or,$a(\cos \theta -\mu \sin \theta )=g(\mu \cos \theta +\sin \theta )$
$\therefore a=\frac{g(\mu \cos \theta +\sin \theta )}{(\cos \theta -\mu \sin \theta )}$