Q. A string is wrapped over a uniform cylinder, as shown in diagram (side view). When cylinder is released, string unwraps without any slipping and cylinder comes down. Which of the following is true ?

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A

Work done by Tension force on the cylinder is zero

B

Work done by the Tension is negative

C

Ratio of rotational kinetic energy and translational kinetic energy is $\frac{1}{2}$

D

Ratio of rotational kinetic energy to translational kinetic energy is 2

Solution:

When cylinder comes down, at the point where string leaves contact with the cylinder is point of instantaneous rest, thus string does zero work.
$\frac{K_{R}}{K_{T}}=\frac{\frac{1}{2} I_{C} \omega^{2}}{\frac{1}{2} m v^{2}}$
$=\frac{\frac{1}{2}\left(\frac{m R^{2}}{2}\right)\left(\frac{v}{R}\right)^{2}}{\frac{1}{2} m v^{2}}=\frac{1}{2}$

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