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Question

A solid sphere of mass 2 kg and diameter 10 cm is rolling without slipping at a speed of 5 ms1. The rotational kinetic energy of the sphere will be

A
10 J
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B
30 J
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C
50 J
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D
70 J
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Solution

The correct option is A 10 J
Rotational kinetic energy, KERot=12ICMω2
Moment of inertia of the solid sphere about the axis passing through it's COM is:
ICM=25mr2, m=2 kg, r=5 cm=0.05 m
Applying condition of pure rolling(v=rω)
KERot=12(25×2×(0.05)2)ω2
KERot=25×(0.05)2×v20.052
KERot=25×25=10 J

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