Question

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

Answer 1

Correct Answer - 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)`