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 statements are correct
B. Only I, II and IV are correct
C. Only II and V are correct
D. Only II and IV are correct

Answer

B

Explanation

Before cutting the string, the tension in string joining m4 and ground is
`T = (m_(1) + m_(2) - m_(3) - m_(4)) g`
and the spring force in the spring joining `m_(3)` and `m_(4)` is `T + m_(4)g`.
As the string is cut the spring force doesn’t 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))`