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A planet moving along an elliptical orbit is closest to the sun at a distance of r₁

A planet moving along an elliptical orbit is closest to the sun at a distance of r₁. If v₁ and v₂ are the linear velocities at these points respectively then the ratio v₁ / v₂ is

Options

(a) ( r₁ / r₂)²
(b) r₂ / r₁
(c) (r₂ / r₁)²
(d) r₁ / r₂

Correct Answer:

r₂ / r₁

Explanation:

Angular momentum is conserved
L₁ = L₂ ⇒ mr₁v₁ = mr₂v₂ ⇒ r₁v₁ = r₂v₂
⇒ v₁ / v₂ = r₂ / r₁

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