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Question

A sphere of mass m is rolling on a frictionless surface (as shown in the figure) with a translation velocity v m/s. The sphere will climb on the inclined plane if v is


A
57gh
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B
2gh
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C
107gh
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D
gh
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Solution

The correct option is C 107gh
The sphere will climb on the inclined plane when
Total energy of the sphere is mgh
Since the sphere have translational as well as rotational motion.
Total energy of the sphere = Rotational kinetic energy+Translational kinetic energy
TE=12Iω2+12mv2
(ω= angular speed of sphere)

12Iω2+12mv2mgh

12(25mr2)ω2+12mv2mgh
For pure rolling, v=rω
15mv2+12mv2mghv107gh

Why this question?

Tips:- A rolling body contains rotational as well as translational kinetic energy.

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