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The moments of inertia of two rotating b...

The moments of inertia of two rotating bodies A and B are `I_(A)` and `I_(B). (I_(A) gt I_(B))` and their angular momenta are equal. Which one has greater `K.E.` ?

A

`K_(1)=K_(2)`

B

`K_(1) lt K_(2)`

C

`K_(1) gt K_(2)`

D

`K_(1)=(1)/(2)K`

Text Solution

Verified by Experts

The correct Answer is:
B
Since the angular momenta are equal
`therefore I_(1)omega_(1)=I_(2)omega_(2)" but "I_(1) gt I_(2)" "therefore omega_(1) lt omega_(2)`
`"K.E. of A "=(1)/(2)I_(1)omega_(1)^(2)=(1)/(2)(I_(1)omega_(1))omega_(1)`
`"K.E. of B"=(1)/(2)(I_(2) omega_(2))omega_(2)" But "I_(1)omega_(1)=I_(2)omega_(2)`
`because omega_(1) lt omega_(2)" "therefore K_(1) lt K_(2)`
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