Question

Three blocks $A$ , $B$ and $C$ of equal mass $m$ are placed one over the other on a smooth horizontal ground as shown in the figure. Coefficient of friction between any two blocks is $0.5$ . The maximum value of the mass of block $D$ so that the blocks $A$ , $B$ and $C$ move without slipping over each other is

• A. $6m$
• B. $5m$
• C. $3m$
• D. $4m$

Answer 1

Answer: (C)

Blocks $A$ and $C$ both move due to friction. But less friction is available to $A$ as compared to $C$ because the normal reaction between $A$ and $B$ is less. Maximum friction between $A$ and $B$ can be
$f_{max}=\mu m_{A}g=\left(\frac{1}{2}\right)mg$
$\therefore$ Maximum acceleration of $A$ can be
$a_{max}=\frac{f_{max}}{m}=\frac{g}{2}$
Further $a_{max}=\frac{m_{D}g}{3m+m_D}$
Or $\frac{g}{2}=\frac{m_{D}g}{3m+m_D}$
Or $m_D=3m$