TS EAMCET · Physics · Laws of Motion

Two identical blocks \(A\) and \(B\), each of mass \(m\) resting on smooth floor, are connected by a light spring of natural length \(L\) and the spring constant \(k\), with the spring at its natural length. \(A\) third identical block \(C\) (mass \(m\) ) moving with a speed \((v)\) along the line joining \(A\) and \(B\) collides with \(A\). The maximum compression in the spring is proportional to

A \(v \sqrt{\frac{m}{2 k}}\)
B \(m \sqrt{\frac{v}{2 k}}\)
C \(\sqrt{\frac{m v}{k}}\)
D \(\frac{m v}{2 k}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(v \sqrt{\frac{m}{2 k}}\)

Step-by-step Solution

Detailed explanation

When block \((C)\) strikes the block \((A)\), then it begins to oscillate, whose time period \(T=2 \pi \sqrt{\frac{m}{2 k}}\) Compression, \(x=v T=v \times 2 \pi \sqrt{\frac{\mu}{2 k}}\) \(\therefore \quad x \propto v \sqrt{\frac{m}{2 k}}\)

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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