Question

Two blocks of equal mass $2M$ are connected by a string and are kept on a rough horizontal surface as shown in the figure. $\mu$ is the coefficient of friction between the blocks and the surface. If $0<F_1-F_2<4\mu Mg$ , then choose the correct statement.

• A. The direction of friction on block $A$ is towards right.
• B. The direction of friction on block $B$ is either towards left or right
• C. Tension in the string is zero
• D. Friction force on block $B$ is zero

Answer 1

The correct option is B The direction of friction on block $B$ is either towards left or right

Since, it is given that $0<F_1-F_2<4\mu Mg$
$\Rightarrow F_1>F_2$
So, block A is the driving block and block B is driven block.
Maximum opposing force on the blocks $=\mu (2M+2M)g=4\mu Mg$
As $F_1–F_2<4\mu Mg$, so system will not accelerate.

If $f_1$ is friction on $A$, it will act towards left to oppose $F_1$.
For $A$: $F_1-f_1=T$
Thus, $T$ can be zero or non zero.
For $B$: $T-F_2=f_2$ where $f_2$ is friction on $B$
Depending on if $T$ is greater or lesser than $F_2$, $f_2$ can act towards left or right.

Hence, only option B is correct.