The distance of the two planets from the Sun are `10^(13)m` and `10^(12) m`, respectively. Find the ratio of time periods and speeds of the two planets.

Options

A. `10`
B. `sqrt(10)`
C. `1/(sqrt(10))`
D. `10^(25)`

Answer

C

Explanation

The time period of satellite is
`T^(2)=kr^(3)`
`impliesT=kr^(3/2)`
or `(T_(1))/(T_(2))=((r_(1))/(r_(2)))^(3/2)`
If `v_(1)` and `v_(2)` be the orbital speeds of the planets
`v_(1)=(2pir_(1))/(T_(1))`
and `v_(2)=(2pir_(2))/(T_(2))`
`:.(v_(1))/(v_(2))=(r_(1))/(r_(2))xx(T_(2))/(T_(1))`
`=(r_(1))/(r_(2))((r_(2))/(r_(1)))^(3/2)=((r_(2))/(r_(1)))^(1/2)`
`=((10^(12))/(10^(13)))^(1/2)=1/(sqrt(10))`