A planet moves around the sun. at a given point `P`, it is closest from the sun at a distance `d_(1)`, and has a speed `V_(1)`. At another point `Q`, when it is farthest from the sun at a distance `d_(2)`, its speed will be

Options

A. `d_(1)^(2) v_(1) // d_(2)^(2)`
B. `d_(2) v_(1) // d_(1)`
C. `d_(1) v_(1) // d_(2)`
D. `d_(2)^(2) v_(1) // d_(1)^(2))`

Answer

C

Explanation

In planetary motion `vec(tau)_("ext".) = 0 rArr vec(L)` = constant
`vec(L) = vec(r) xx vec(p) (= vec(mv)) = mrv (because theta = 90^(@))`
So `m_(1) d_(1) v_(1) = m_(2) d_(2) v_(2) `(here r = d )
`rArr v_(2) = (v_(1)d)/(d_(2))`
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