The reel shown in figure has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its un-stretched position and the reel is then released from rest. The angular speed of the reel when the spring is again un-stretched is

# The reel shown in figure has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle and the incline are frictionless. The reel is wound counterclockwise so that the spring stretches a distance d from its un-stretched position and the reel is then released from rest. The angular speed of the reel when the spring is again un-stretched is

1. A

2. B

3. C

4. D

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### Solution:

The block and end of the spring are pulled a distance d up the incline and then released. The angular speed of the reel and the speed of the block are related by v = $\mathrm{\omega }$R. The block-reel-Earth system is isolated, so

$\left(\frac{1}{2}{\mathrm{mv}}^{2}-0\right)+\left(\frac{1}{2}{\mathrm{I\omega }}^{2}-0\right)$+

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