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Question

A wheel of mass m=1 kg and radius r=1 m is under pure rolling in a straight line as shown in figure.



If V=2 m/s, a=1 m/s2, α=1 rad/s2 and ω=2 rad/s, find the torque and K.E of the wheel about the contact point.

A
τC=2 N-m, K.E=1 J
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B
τC=1 N-m, K.E=2 J
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C
τC=2 N-m, K.E=4 J
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D
τC=3 N-m, K.E=5 J
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Solution

The correct option is C τC=2 N-m, K.E=4 J


Let moment of inertia about contact point be IC.
Using parallel axis theorem,
IC=ICOM+mr2
=mr2+mr2=2mr2
=2×1×1 kg-m2
IC=2 kg-m2

We know that,
τC=ICα=(2×1) N-m=2 N-m
and
K.E=12ICω2=12×2×22
K.E=4 J
So, option (c) is correct.

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