Question

The figure shows an $L$ shaped body of mass $M$ placed on smooth horizontal surface. The block $A$ is connected to the body by means of an inextensible string, which is passing over a smooth pulley of negligible mass. Another block $B$ of mass $m$ is placed against a vertical wall of the body. Find the minimum value of the mass of block $A$ so that block $B$ remains stationary relative to the wall. Coefficient of friction between the block $B$ and the vertical wall is $\mu =2.(Takeg=10m/s^2)$

• A. $m_A=\frac{M+m}{\mu -1}but\mu >1$
• B. $m_A=\frac{M+m}{\mu +1}$
• C. $m_A=\frac{M}{\mu -1}but\mu >1$
• D. $m_A=\frac{m}{\mu -1}but\mu >1$

Answer 1

The correct option is A $m_A=\frac{M+m}{\mu -1}but\mu >1$

For mass $m$ to remain stationary w.r.t. wall, the friction force should balance gravity force.

Analyzing the motion of block in non inertial frame of reference, applying pseudo force $ma$ on block, where $a$ is acceleration of the system.

$m_{A}g-T=m_{A}aT=(M+m)a\Rightarrow a=\frac{m_{A}g}{m_A+m+M}$

From FBD of block $m$

In horizontal direction,

$N=ma$

in vertical direction,

$mg=f=\mu N$

$mg=\mu m\frac{m_{A}g}{m_A+m+M}\Rightarrow m_A=\frac{M+m}{\mu -1}$