Question

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

• A. $0.8\text{g}$
• B. $0.4\text{g}$
• C. $0.5\text{g}$
• D. Zero

Answer 1

The correct option is B $0.4\text{g}$

Let acceleration of both blocks be $a$

From FBD of block on rough surface
$N=mg=g$
$T-f=ma$
$T-\mu N=a$
$T-\mu g=a$
$T-0.2g=a...........\left(1\right)$
From FBD of hanging block
$1g-T=1a................\left(2\right)$
Adding $\left(1\right)$ and $\left(2\right)$
$\Rightarrow 0.8g=2a$
$\Rightarrow a=0.4{gm/s}^2$
The correct option is (b)