A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the sun is `r_(min)`. The farthest distance from the sun is `r_(max)` if the orbital angular velocity of the planet when it is nearest to the Sun `omega` then the orbital angular velocity at the point when it i at the farthest distanec from the sun is

Options

A. `sqrt((r_(min) // r_(max))) omega`
B. `sqrt((r_(max) // r_(min))) omega`
C. `sqrt((r_(max^(2)) // r_(min^(2) ))) omega`
D. `sqrt((r_(min^(2)) // r_(max^(2)))) omega`

Answer

D

Explanation

`v_(1) r_(1) = v_(2) r_(2) or r_(1)^(2) omega_(1) = r_(2)^(2) omega_(2) ( because "L = mrv = constant")`
or `r_("min")^(2) omega = r_("max")^(2) omega. " " therefore omega. = (r_("min")^(2) // r_("max")^(2)) omega`