Question

A pulley mass arrangement is shown is the figure. A force of $50\text{N}$ is applied on the $2\text{kg}$ block. Find the acceleration of COM of the system.

• A. $1.6{\text{m/s}}^2$
• B. $2{\text{m/s}}^2$
• C. $10{\text{m/s}}^2$
• D. $0{\text{m/s}}^2$

Answer 1

The correct option is A $1.6{\text{m/s}}^2$

FBD of blocks $2\text{kg}$ and $3\text{kg}$ :


For $2\text{kg}$ block:

$(50+2g)-T=m_{2}a$
$50+2\times 10-T=2a$
$\Rightarrow 70-T=2a...\left(1\right)$

For $3\text{kg}$ block:

$T-3g=m_{1}a\Rightarrow T-30=3a...\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$70-30=5a$
$40=5a\Rightarrow a=8{\text{m/s}}^2$

Therefore, accerlation of $3\text{kg}$ block is upward and acceleration of $2\text{kg}$ block is downwards.
Acceleration of COM,
$a_{com}=\frac{m_1{a}_1+m_2{a}_2}{m_1+m_2}=\frac{3\times 8+2\times (-8)}{5}=1.6{\text{m/s}}^2$ [Taking upwards motion as positive ]

Hence, option (a) is the correct answer.