question_answer

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

Correct Answer: A

Solution :

Free body diagram of the two bodies are as follows

Let acceleration of both the blocks towards left is a. Then

\[a=\frac{f-2}{2}=\frac{20-f}{4}\] or \[2f-4=20-f\] or \[f=8N\]

Maximum friction between the two blocks can be:

\[{{f}_{\max }}=\mu mg\left( m=2kg \right)\]

\[=\left( 0.5 \right)\left( 2 \right)\left( 10 \right)=10N\]

Now since \[f<{{f}_{\max }}\]

Therefore, friction force between the two blocks is 8N.