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Astronomers observe two separate solar s...

Astronomers observe two separate solar systems each consisting of a planet orbiting a sun. The two orbits are circular and have the same radius `R`. It is determined that the planets have angular momenta of the same magnitude `L` about their suns, and that the orbital periods are in the ratio of three to one, i.e. `T_(1)=3T_(2)`. The ratio `m_(1)//m_(2)` of the masses of the two planets is

A

`1`

B

`sqrt(3)`

C

`2`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
D
`L=mVr v=(2piR)/T`
`L=mR((2piR)/T)=(2pimR^(2))/T`
`(L_(1))/(L_(2))=(m_(1))/(T_(1)) (T_(2))/(m_(2))implies(m_(1))/(m_(2))=(T_(1))/(T_(2))=3`
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