Question

In the arrangement shown in the figure, coefficient of friction between the two blocks is, $\mu =0.5$. The force of friction acting between the two blocks is

• A. $8\text{N}$
• B. $10\text{N}$
• C. $6\text{N}$
• D. $4\text{N}$

Answer 1

The correct option is A $8\text{N}$

Free body diagram of the two bodies are as follows


Let us assume that the two blocks move together with common acceleration towards left is $a_c$.
Then, $a_c=\frac{f-2}{2}=\frac{20-f}{4}$
or, $2f-4=20-f$
or, $f=8\text{N}$
Maximum friction between the two blocks can be
$f_{\text{max}}=\mu m_{A}g=\left(0.5\right)\left(2\right)\left(10\right)=10\text{N}$
Since, $f<f_{\text{max}}$, it means our assumtion is right
Therefore, friction force between the two blocks is $f=8\text{N}$