Question

Two blocks are attached to the pulley as shown in the arrangement.

If the string is inextensible and all surfaces are frictionless, find out the magnitude acceleration of COM of the system. (Take $g=10m/s^2$)

• A. $1.6{\text{m/s}}^2$
• B. $0.4{\text{m/s}}^2$
• C. $0.16{\text{m/s}}^2$
• D. $4{\text{m/s}}^2$

Answer 1

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

FBD's of blocks

For block $A$,
$m_{A}g-T=m_{A}a$
$\Rightarrow 7g-T=7a------\left(1\right)$
For block $B$,
$T-m_{B}g=m_{B}a$
$\Rightarrow T=3g+3a------\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we have
$7g-(3g+3a)=7a$
$\Rightarrow 4g=3a+7a=10a$
$a=4{\text{m/s}}^2$
Now, acceleration of COM
$a_{com}=\frac{m_{A}a+m_{B}a}{m_A+m_B}=\frac{7\times (-4)+3\times \left(4\right)}{10}$
$a_{com}=\frac{-16}{10}=-1.6{\text{m/s}}^2$
In magnitude, $a_{com}=1.6{\text{m/s}}^2$