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Question

A hollow vertical cylinder of radius R and height h has smooth internal surface. A small particle is placed in contact with the inner side of the upper rim at a point P. It is given a horizontal speed v0 tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will be

A
h2πR
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B
v02gh
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C
2πRh
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D
v02πR(2hg)
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Solution

The correct option is D v02πR(2hg)

The vertical distance covered by a particle during travel from P to Q is h.

Let it takes time t to come out from Q.

For vertical motion only, uy=0

And from equation of motion,

h=12gt2

t=2hg

Since the internal surface of cylinder is smooth, it will move with the same speed v0 throughout its journey.

Let n be the total number of revolutions made by the particle. So,

n(2πR)=v0×t

n=v0t2πR

n=v02πR2hg

Hence, option (d) is correct.
Why this question ?
Tip : During the entire journey total distance covered can be visualized as number of revolution times the circumference of circular path.

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