Question

Two blocks are resting on ground with masses $m_1$ and $m_2$. A string connects them which goes over a mass less pulley $P$. There is no friction between pulley and string. A force $F$ is applied on pulley $P$. The acceleration of centre of mass of blocks is:
(Given that $T=2m_{1}g$ and $m_2=3m_1)$.

• A. $g/8$
• B. $g/4$
• C. $\frac{g}{2}$
• D. $g$

Answer 1

Answer: (B)

$g/4$

According to the question,
$T=2m_{1}g$
Thus, $m_2$ will not be lifted.
Hence, its acceleration $a_2=0$
For $m_1,T-m_{1}g=m_1{a}_1$
$\Rightarrow a_1=\frac{2m_{1}g-m_{1}g}{m_1}=g$
$a_{cm}=\frac{m_1{a}_1+m_2{a}_2}{m_1+m_2}=\frac{m_1{a}_1+0}{m_1+m_2}=\frac{m_{1}g}{m_1+3m_1}=\frac{g}{4}$.