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.

Options

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 given data.

Answer

C

Explanation

( c) `I_A omega_A = I_B omega_B` (Given)
:. `(omega_A)/(omega_A) = (I_B)/(I_A)` …(i)
Kinetic energy `= (1)/(2) I omega^2`
:. `((K.E.)_A)/((K.E.)_B) = ((1)/(2) I_A omega_A^2)/((1)/(2) I_B omega_B^2)`
=`(I_A)/(I_B)xx ((I_B)/(I_A))^2` (Given (i))
=`(I_B)/(I_A)`
As `I_A gt I_B` (Given)
:. `(K.E.)_A lt (K.E.)_B`.