Question

Two blocks of masses $m$ and $2m$ are placed one over the other as shown in the figure. The coefficient of friction between $m$ and $2m$ is $\mu $ and between $2m$ and ground is $\frac{\mu }{3}$ . If a horizontal force $F$ is applied on the upper block and $T$ is the tension developed in the string, then choose the incorrect alternative.

• A. If $F=\frac{\mu }{3}mg,T=0$
• B. If $F=\mu mg,T=0$
• C. If $F=2\mu mg,T=\frac{\mu m g}{3}$
• D. If $F=3\mu mg,T=0$

Answer 1

Answer: (C)

The maximum frictional force on $1^{s t}$ block due to $2^{n d}$ block is acting towards left as the accelerating force is acting towards the right. Its value is $f_{1 m a x}=μmg$
Now for $2^{n d}$ body, $f_{1}$ acting towards right is responsible to move block towards the right, but $f_{2}$ will act towards the left to hold the body in rest. Its value is
$f_{2 m a x}=\frac{\mu }{3}\left(3 \, m g\right)=μmg$

$T+f_{2}=f_{1}$
$T+\mu mg =\mu mg$
$T=0$
$\Rightarrow $ Tension will be zero in all circumstances. Hence A, B and D all the three are correct.
Note- In the second block, we can very clearly see that T=0. It is independent of the force applied as $2^{n d}$ block is free from any external force.