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. $6 \, m$
• B. $5 \, m$
• C. $3 \, m$
• D. $4 \, m$

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
$f_{m a x}=\mu \, m_{A}g=\left(\frac{1}{2}\right)mg$
$\therefore $ Maximum acceleration of $A$ can be
$a_{m a x}=\frac{f_{m a x}}{m}=\frac{g}{2}$
Further $a_{m a x}=\frac{m_{D} g}{3 m + m_{D}}$
Or $\frac{g}{2}=\frac{m_{D} g}{3 m + m_{D}}$
Or $m_{D}=3m$