Question

In the arrangement shown in figure, coefficient of friction between the two blocks is $\mu=\frac{1}{2}$. The force of friction acting between the two blocks is

• A. 8 N
• B. 10 N
• C. 6 N
• D. 4 N

Answer 1

Answer: (A)

Let $f$ be the force of friction between the two blocks.
Let $a$ be the acceleration of the two blocks to the left. The free
body diagrams of two blocks are shown in the figure.

Their equations of motion are
$f-2=2 a\,\,\, ...(i)$
$20-f=4 a\,\,\, ...(ii)$
Solving $(i)$ and $(ii)$ , we get $f=8 N$
Maximum force of friction, $f_{\max }=\mu m g=\frac{1}{2} \times 2 \times 10=10\, N$
As the blocks move together, $f < f_{\max }$
$\therefore f=8 N$