Question

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure.
The wedge is inclined at $45^{\circ }$ to the horizontal on both the sides. If the coefficient of friction between the block $A$ and the wedge is $2/3$ and that between the block $B$ and the wedge is $1/3$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

• A. $-1m{s}^{-2}$
• B. $-1.2m{s}^{-2}$
• C. $-0.2m{s}^{-2}$
• D. zero

Answer 1

Answer: (D)

Total maximum friction force, $f_t=f_A+f_B$
${\mu }_{A}mg\cos 45^{\circ }+{\mu }_{B}2mg\cos 45^{\circ }$
or, $f_t=mg\left(\frac{2}{3}\times \frac{1}{\sqrt{2}}+\frac{1}{3}\times 2\times \frac{1}{\sqrt{2}}\right)$
$=\frac{4}{3\sqrt{2}}mg$
The net pulling force, $F=2mg\sin 45^{\circ }-mg\sin 45^{\circ }$
$=mg\sin 45^{\circ }$
$=\frac{mg}{\sqrt{2}}$
$\because F<f_t$
$\therefore$ The blocks will not move.
So, acceleration of block $A$ is Zero.