The maximum and minimum distances of a comet from the sun are `1.4xx10^(12)m` and `7xx10^(10)m`. If its velocity nearst to the sun is `6xx10^(4)ms^(-1)`, what is the velocity in the farthest position? Assume that path of the comet in both the instantaneous positions is circular.

Explanation

At minimum distance `r_(1)=7xx10^(10)m`
Velocity `v_(1)=6xx10^(4)ms^(-1)`
At maximumdistance `r_(2)=1.4xx10^(12)m`, ,
velocity `v_(2)=?`
By conservation of angular momentum,
`I_(1)omega_(1)=I_(2)omega_(2)`
or `mr_(1)^(2)xx(v_(1))/(r_(1))=mr_(2)^(2)xx(v_(2))/(r_(2))`
or `v_(1)r_(1)=v_(2)r_(2)`
Velocity in teh farthest position
or `v_(2)=(v_(1)r_(1))/(r_(2))=(6xx10^(4)xx7xx10^(10))/(1.4xx10^(12))`
`=3000ms^(-1)`