Question

A planet moving along an elliptical orbit is closest to the sun at a distance r₁ and farthest away at a distance of r₂. If v₁ and v₂ are the liner velocities at these points respectively, then the ratio (v₁ / v₂) is ……….. 

(A) (r₁ / r₂) 

(B) (r₁ / r₂)² 

(C) (r₂ / r₁) 

(D) (r₂ / r₁)²

Answer 1

Correct option: (C) (r₂ / r₁)

Explanation:

by conservation of angular momentum.

mass × orbital velocity × radius = constant

i.e.  mVr = constant

since m remains same,

Vr = constant

i.e.   V ∝ (1/r)

∴  V₁r₁ = V₂r₂  

∴  (V₁ / V₂) = (r₂ / r₁)