Question

A block of mass $1kg$ is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown. Another block of $1kg$ is connected to the other end of the string. The accleration of the system is (coefficient of friction $\mu =0.2$)

• A. $0.8g$
• B. $0.4g$
• C. $0.5g$
• D. Zero

Answer 1

The correct option is B $0.4g$

FBD for the block kept on the rough surface

$T-(0.2\times 1\times g)=(1\times a)$ ..(i)
$T=0.2g+a$
FBD for the hanging block

Now by Newton's second law
$g-T=a$
$\begin{array}{}T=g-a& \text{(ii)}\end{array}$
By eleminating $T$ and calculating acceleration we get,
$0.2g+a=g-a$
$0.8g=2a$
$a=0.4g$