Question

Immediately on cutting the taut string, the acceleration of one of the blocks is found to be $2m{s}^{-2}.$ If $m_1=6kg,m_2$ is equal to $(g=10m{s}^{-2})$

• A. $4kg$
• B. $5kg$
• C. $2kg$
• D. $8kg$

Answer 1

The correct option is B $5kg$

At rest,
$T^{\prime }=(m_1-m_2)g$
$\therefore m_1>m_2$
On cutting $T^{\prime }=0$,


hence net force on $m_2$ is $(m_1-m_2)g$
$m_{2}a=\left(m_1-m_2\right)g$
$\therefore a=\left(\frac{m_1-m_2}{m_2}\right)g$ (upwards)
After cutting the string spring force doesn't change , so $m_1$ 's acceleration is zero.
$\therefore \left(\frac{m_1-m_2}{m_2}\right)g=2$$(\because a=2)$
$\Rightarrow \frac{m_1}{m_2}=1.2$
$\Rightarrow \frac{6}{m_2}=1.2$
$m_2=5kg$