The moments of inertia of two rotating bodies A and B 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 the given data.

Answer

C

Explanation

`I_(A) omega_(A) = I_(B) omega_(B) , therefore (omega_(A))/(omega_(B)) = (I_(B))/(I_(A)) " " … (i)`
Kinetic energy = `(1)/(2) I omega^(2)`
`therefore ((KE)_(A))/((KE)_(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)= (I_(B))/(I_(A)) " "` (Using (i))
As `I_(A) gt I_(B)` (Given) , `therefore (KE)_(A) lt (KE)_(B)`