Three blocks A, B and C of equal mass m are placed on a smooth su… - Vidyadip

MCQ

Three blocks $A$, $B$ and $C$ of equal mass $m$ are placed on a smooth surface as shown. Coefficient of friction between any block $A, B$ and $C$ is $μ$. The maximum value of mass $D$ so the block $A, B$ & $C$ move without slipping over each other is

A
$\frac{{3m\mu }}{{\mu \, + \,1}}$
B
$\frac{{3m(1 - \mu )}}{{\mu \,}}$
C
$\frac{{3m(1 + \mu )}}{{\mu \,}}$
✓
$\frac{{3m\mu }}{{(1 \, - \,\mu)}}$

✓

Answer

Correct option: D.

$\frac{{3m\mu }}{{(1 \, - \,\mu)}}$

d
Maximum acceleration of $\mathrm{B}$ of $\mathrm{C}$ can be $\mathrm{mgso}$ that they do not slip with each other or $A$

For the system of $(A+B+C)$

$T=3 m a=3 \mu m g$

For $D$

$M g-T=M a$

$\Rightarrow M g-3 \mu m g=M \mu g$

$\Rightarrow M=\frac{3 \mu m}{1-\mu}$

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