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 ($g=10m{s}^{-1}$)

• A. $8N$
• B. $10N$
• C. $6N$
• D. $4N$

Answer 1

The correct option is A $8N$

The maximum force of friction that can occur between the two blocks is
$f{}_{max}=\mu mg$ = $\frac{1}{2}\times 2\times 10$ = $10N$
The acceleration of the system is $\frac{sumoftheforces}{sumofthemasses}$ = $\frac{20+(-2)}{4+2}$ =$3m{s}^{-2}$
The system of blocks has an acceleration in the left side. The force of friction opposing the motion of the $2kg$ block in the left side is $ma$ $+$ $force$ $acting$ $in$ $the$ $direction$ $of$ $friction$ = $(2kg\times 3m{s}^{-2})+2N$ =$8N$. Thus the force of friction acting between the two blocks is $8N$.