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Two uniform spheres of mass M have radii...

Two uniform spheres of mass `M` have radii `R` and `2 R`. Each sphere is rotating about a fixed axis through a diameter, the rotational kinetic energies of the sphere are identical. What is the ratio of the magnitude of the angular momentum of these spheres gt That is, `(L_(2 R))/(L_( R)) =`

A

4

B

`2 sqrt(2)`

C

2

D

`sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`KE = (L^(2))/(2I)`
`L = sqrt(2I(K.E)) rArr (L_(2R))/(L_(R)) = sqrt((I_(2R))/(I_(R))) = sqrt(((2)/(5) xx m(2R)^(2))/((2)/(5) mR^(2)))`
`(L_(2R))/(L_(R)) = (2)/(1)`.
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