Two rigid bodies `A` and `B` rotate with angular momenta `L_(A)` and `L_(B)` respectively. The moments of inertia of `A` and `B` about the axes of rotation are `I_(A)` and `I_(B)` respectively. If `I_(A)=I_(B)//4` and `L_(A)=5L_(B)`, then the ratio of rotational kinetic energy `K_(A)` of `A` to the rotational kinetic energy `K_(B)` of `B` is given by

Options

A. `(K_(A))/(K_(B))=25/4`
B. `(K_(A))/(K_(B))=5/4`
C. `(K_(A))/(K_(B))=1/4`
D. `(K_(A))/(K_(B))=100`

Answer

D

Explanation

`K_(A)=(L_(A)^(2))/(2l_(A))=(25L_(B)^(2))/(2l_(B))`
`K+B=(L_(B)^(2))/(2l_(B))`
Now, `(K_(A))/(K_(B))=25xx4=100`