Two rotating bodies A and B masses m and 2m with moment of inertia `I_(A) and I_(B) (I_(B)gtI_(A))` have equal kinetic energy of rotation. If `L_(A)andL_(B)` be their angular moment respectively, then …….

Options

A. `L_(B)gtL_(A)`
B. `L_(A)gtL_(B)`
C. `L_(A)=(L_(B))/(2)`
D. `L_(A)=2L_(B)`

Answer

A

Explanation

Rotational kinetic energy `K=(1)/(2)Iomega^(2)`
`therefore K=(I^(2)omega^(2))/(2I)`
`therefore K=(L^(2))/(2I)[because Iomega=L]`
but if kinetic energy of rotation is same
`IpropL^(2)`
`therefore (I_(B))/(I_(A))=(L_(B)^(2))/(L_(A)^(2))`
but `I_(B)gtI_(A)`
`therefore (L_(B)^(2))/(L_(A)^(2))gt1`
`therefore (L_(B))/(L_(A))gt1`
`therefore L_(B)gtL_(A)`