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The moments of inertia of two rotating b...

The moments of inertia of two rotating bodies `A` and are `I_A` and `I_B(I_A gt I_B)`. If their angular momenta are equal then.

A

Kinetic energy of A = Kinetic energy of B

B

Kinetic energy of A `gt` Kinetic energy of B

C

Kinetic energy of A `lt` Kinetic energy of B

D

Kinetic energy of the two bodies cannot be compared with the given data

Text Solution

Verified by Experts

The correct Answer is:
C
`I_(A)omega_(A) = I_(B)omega_(B)` (Given)
`therefore (omega_(A))/(omega_(B)) = I_(B)/I_(A)`……………..(i)
Kinetic energy `=1/2 Iomega^(2)`
`therefore (K.E)_(A)/(K.E)_(B) = (1/2 I_(A)omega_(A)^(2))/(1/2I_(B)omega_(B)^(2)) = (I_(A))/(I_(B)) xx (I_(B)/I_(A))^(2)` (Using (i))
`=I_(B)/I_(A)`
As `I_(A) gt I_(B)` (given)
`therefore (K.E)_(A) lt (K.E)_(B)`
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