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 :

Two bodies have their moment of inertia I and 2I respectively about th

1.	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 :
Answer» `2:1` `1:2` `sqrt(2):1` `1:sqrt(2)` Solution :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)`