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A light elastic cord of stiffness k and natural length $l$ is suspended from the ceiling. A bead of mass m threaded on the cord is held motionless close to the ceiling and released. If the bead eventually slides down the cord with a constant speed v relative to the ceiling, which option(s) are correct for the instant when the bead has travelled a distance x from the ceiling where it was released:( g is acceleration due to gravity)

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Elongation in the cord is $\frac{mgx}{mg + k l}$

Elastic potential energy stored in the cord is $\frac{m^{2} g^{2} x}{(mg + k l)}$ (assume elastic potential energy stored to be zero when it is relaxed)

Instantaneous value of thermal power dissipated is $(\frac{mg + 2 k l}{mg + k l}) \frac{mgv}{2}$

Time taken by the bead to reach the given point from beginning is $\frac{x}{3 v}$

answer is C, D.

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Detailed Solution

$k' = \frac{mg + k l}{x}$

$e = \frac{mg}{k'}$

$U = \frac{m^{2} g^{2}}{2 k'}$

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