Question

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

• A. $zero$
• B. $1{ms}^{-1}$
• C. $2{ms}^{-1}$
• D. $3{ms}^{-1}$

Answer 1

The correct option is A $zero$

Total maximum friction force ,$f_t=f_A+f_B={\mu }_A\mu mg\cos {45}^o+{\mu }_{B}2mg\cos {45}^o$
or $f_t=mg(\frac{2}{3}.\frac{1}{\sqrt{2}}+\frac{1}{3}.2.\frac{1}{\sqrt{2}})=\frac{4}{3\sqrt{2}}mg$
The net pulling force , $F=2mg\sin {45}^o-mg\sin {45}^o=\frac{mg}{\sqrt{2}}$
Since, $F<f_t$ . thus the blocks will not move. So acceleration of block A is zero.