Two bodies with moment of inertia `l_(1)` and `l_(2)` `(l_(1) gt l_(2))` have equal angular momentum. If `E_(1)` and `E_(2)` are the rotational kinetic energies, then

Options

A. `E_(1)=E_(2)`
B. `E_(1)lt E_(2)`
C. `E_(1)gt E_(2)`
D. `E_(1) gr E_(2)`

Answer

B

Explanation

`K.E._(1)=(1)/(2)(L^(2))/(I_(1))`
`therefore K.E._(1) prop (1)/(I_(1))`
`K.E._(2)=(1)/(2)(L^(2))/(I_(2)) therefore K.E._(2) prop (1)/(I_(2))`
`(K.E._(2))/(K.E._(1))=(I_(1))/(I_(2))`
`therefore K.E._(1) lt K.E._(2)`