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JEE Main 2014 (12 Apr, Shift 1) · Spring & Elastic Energy

Spring & Elastic Energy question from JEE Main 2014 (12 Apr, Shift 1)

Q22JEE Main 2014 · 12 APR · SHIFT 1Difficult

Spring & Elastic Energy

A spring of unstretched length $l$ has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is:

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Answer: (d)

An element at distance $y$ from the fixed end moves with speed $\frac{vy}{l}$ ; its mass is $\frac{m}{l}dy$ .
$K = \int_0^l \frac{1}{2}\frac{m}{l}\left(\frac{vy}{l}\right)^2 dy = \frac{mv^2}{2l^3}\cdot\frac{l^3}{3}$
So the answer is (d) $\frac{1}{6}mv^2$ .

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