For the system shown in fog. `m_(1) gt m_(2) gtm_(3) gt 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 four blocks can be determined.
Statement III: Only `m_(4)` remain stationary.
Statement IV: Only `m_(4)` accelerates.

Options

A. All the statement are correct.
B. Only I, II and IV are correct.
C. Only I,and II are correct.
D. Only II and IV are correct.

Answer

B

Explanation

Before cutting the string, the tension in string joining `m_(4)` and ground is `T=(m_(1)+m_(2)-m_(3)-m_(4))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=(T+m_(4)g-m_(4)g)/(m_4)`.