Two bodies with moment of inertia `I_1` and `I_2 (I_1 gt I_2)` have equal angular momenta. If their kinetic energy of rotation are `E_1` and `E_2` respectively, then.

Options

A. `E_(1)=E_(2)`
B. `E_(1)ltE_(2)`
C. `E_(1)gtE_(2)`
D. `E_(1)geE_(2)`

Answer

B

Explanation

`E_(1)=1/2 I_(I)1omega_(1)^(2)=1/2(I_(1)omega_(1))omega_(1)=1/2komega_(1)`
Now `I_(1)omega_(1)=I_(2)omega_(2)=k` (say)
`E_(2)=1/2I_(2)omega_(2)^(2)=1/2(I_(2)omega_(2))omega_(2)=1/2komega_(2)`
`I_(1)gtI_(2)` and `omega_(2) gt omega_(1)`
so `E_(2)gtE_(1)`