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 $μ$ and between $2m$ and ground is $\frac{μ}{3}$ . 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 $F=\frac{μ}{3}mg,T=0$
• B. If $F=μmg,T=0$
• C. If $F=2μmg,T=\frac{μmg}{3}$
• D. If $F=3μmg,T=0$

Answer 1

Answer: (C)

The maximum frictional force on $1^{st}$ block due to $2^{nd}$ block is acting towards left as the accelerating force is acting towards the right. Its value is $f_{1max}=μmg$
Now for $2^{nd}$ 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
$f_{2max}=\frac{μ}{3}\left(3mg\right)=μmg$

$T+f_2=f_1$
$T+μmg=μmg$
$T=0$
$⇒$ 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 $2^{nd}$ block is free from any external force.