AP 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 \(\frac{m v}{2 k}\)
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, \(x=v T=v \times 2 \pi \sqrt{\frac{\mu}{2 k}}\) \(\therefore \quad x \propto v \sqrt{\frac{m}{2 k}}\)
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