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  • A hollow cylinder rolls from the top of a cliff such that it enters the circular loop starting at the bottom of the cliff. If the cylinder is just able to complete the circular loop, what was the h

A hollow cylinder rolls from the top of a cliff such that it enters the circular loop starting at the bottom of the cliff. If the cylinder is just able to complete the circular loop, what was the height of the cliff from where it started rolling? (Given, the radius of the cylinder is 10 cm, while that of the track is 1 m.)

Option: 1

2.8 m


Option: 2

3.0 m


Option: 3

3.2 cm


Option: 4

2.6 m


Answers (1)

best_answer

Applying energy conservation at points A and B:

mgh = \frac{1}{2} mv^2 + \frac{1}{2} I\omega^2 + mg(2R - r)

gh = \frac{v^2}{2} + \frac{1}{2} r^2\omega^2 + g(2R - r)

2g [h - 2R + r] = 2 v^2

For just able to complete the loop:

v = \sqrt{g(R-r)}

2g[h - 2R +r] = 2g (R-r)

h - 2R +r = R-r

h = 3R -2r

h = 3*1 - 2*0.1 = 2.8 m

Posted by

Divya Prakash Singh

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