Two bodies have their moment of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio :

Options

A. `2:1`
B. `1:2`
C. `sqrt(2):1`
D. `1:sqrt(2)`

Answer

D

Explanation

Rotational kinetic energy `K=(1)/(2)Iomega^(2)`
`=(1)/(2)(Iomega).omega`
`K=(1)/(2)L.omega`
Putting `omega=(L)/(I)`,
`K=(1)/(2)(L^(2))/(I)`
`therefore L^(2)=2KI`
`therefore L=sqrt(2KI)`
Now for first body `L_(1)=sqrt(2K_(1)I_(1))` and for second body `L_(2)=sqrt(2K_(2)I_(2))`
`therefore (L_(1))/(L_(2))=sqrt((2K_(1)I_(1))/(2K_(2)I_(2)))`
Putting `K_(1)=K_(2)=KandI_(2)=2I,I_(1)=I` in equ.
`(L_(1))/(L_(2))=sqrt((KI)/(K(2I)))=sqrt((1)/(2))`
`therefore (L_(1))/(L_(2))=(1)/(sqrt(2))`
`therefore L_(1):L_(2)=1:sqrt(2)`