A circular ring of radius 5 m has moment of inertia of 100 kg-m2 about its natural axis. This ring is converted into a circular disc having same moment of inertia about the disc’s natural axis. What is the radius of the circular disc?
A
10 m
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B
√2 m
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C
5√2 m
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D
5 m
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Solution
The correct option is C5√2 m Radius of ring r=5 m Moment of inertia of ring =IRing=100 kg-m2 ⇒IRing=Mr2⇒100=M×52 ⇒M=10025=4 kg
When the ring is converted into a disc, the mass remains same. ∴ Mass of disc ;M=4 kg Given: Moment of inertia of disc is also same. ∴Idisc=100 kg-m2 ⇒Idisc=MR22 ⇒100=4×R22⇒R2=2004=50 ⇒R=5√2 m