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. `K_(A)=K_(B)`
B. `K_(A) gt K_(B)`
C. `K_(A) lt K_(B)`
D. `K_(A)=(K_(B))/(2)`

Answer

B

Explanation

For A, `K_(A)=(1)/(2)l_(1)omega_(1)^(2)=(1)/(2)(l_(1)omega_(1))omega_(1)`
For B, `K_(B)=(1)/(2)l_(2)omega_(2)^(2)=(1)/(2)(l_(2)omega_(2))omega_(2)`
But it is given that `l_(1)omega_(1)=l_(2)omega_(2)`
`therefore" "(K_(A))/(K_(B))=(omega_(1))/(omega_(2))" but "(l_(2))/(l_(1))=(omega_(1))/(omega_(2))`
`becuase" "l_(2) gt l_(1) therefore omega_(1) gt omega_(2)`
`therefore" From (1), "K_(A) gt K_(B)`