For the system shown in figure, m_1>m_2>m_3 >m_4 . Initially, the… - Vidyadip

MCQ

For the system shown in figure, $m_1>m_2>m_3 >m_4$ . Initially, the system is at rest in equilibrium condition. If the string joining $m_4$ and ground is cut, then just after the string is cut :

Statement $I$ $m_1$ ,$m_2$ ,$m_3$ remain stationary.

Statement $II$ The value of acceleration of all the $4$ blocks can be determined.

Statement $III$ Only $m_4$ remains stationary.

Statement $IV$ Only $m_4$ accelerates.

Statement $V$ All the four blocks remain stationary.

Now, choose the correct option.

A
All the statements are correct
✓
Only $I$ , $II$ and $IV$ are correct
C
Only $II$ and $V$ are correct
D
Only $II$ and $IV$ are correct.

✓

Answer

Correct option: B.

Only $I$ , $II$ and $IV$ are correct

b
Before cutting the string, the tension in string joining $m_{4}$ and ground is $T=\left(m_{1}+m_{2}-m_{3}-m_{4}\right) g$

And the spring force in the spring joing $m_{3}$ and $m_{4}$ is $T-m_{4} g .$

As the string is cut, the spring force do not change instantly, so just after cutting the string the equilibrium of $m_{1}, m_{2}$ and $m_{3}$would be maintained but $m_{4}$ accelerates in upward direction with acceleration given by

$a=\frac{T+m_{4} g-m_{4} g}{m_{4}}$

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