JEE Main · PhysicsHard
A chain of mass $M$ and length $L$ is held on a frictionless table with $\frac{1}{n}$ of its length hanging over the edge. If the chain is released, what is the velocity of the chain when it just leaves the table?
- A.$\sqrt{gL(1 - \frac{1}{n^2})}$
- B.$\sqrt{gL(1 + \frac{1}{n^2})}$
- C.$\sqrt{gL(2 - \frac{1}{n^2})}$
- D.$\sqrt{gL(\frac{1}{n^2})}$
Show correct answer & step-by-step solution
Correct answer: A — $\sqrt{gL(1 - \frac{1}{n^2})}$
Solution
Use the principle of conservation of mechanical energy. The change in potential energy of the center of mass of the chain, , equals the gain in kinetic energy, .
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