TS EAMCET · Physics · Work Power Energy

System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass $2 m$ and $m$ just after the string is cut will be

A $\frac{g}{2}$ upwards, $g$ downwards
B $g$ upwards, $\frac{g}{2}$ downwards
C $g$ upwards, $2 g$ downwards
D $2 g$ upwards, $g$ downwards

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{g}{2}$ upwards, $g$ downwards

Step-by-step Solution

Detailed explanation

Initially, both the blocks were under equilibrium, so for mass m, T=mg, and for mass 2m, Fs=T+2mg=3mg Now, after the string is cut, the tension in it becomes zero. Therefore, for m, mg-0=ma ⇒a=g(downward) and for 2m, 2mg+0-Fs=2mb2mg+0-3mg=2mb⇒b=-g2 i.e., g2…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass 2m and m just after the string is cut will be

Step-by-step Solution

System shown in the figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass $2 m$ and $m$ just after the string is cut will be