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Q.

A planet moves around the sun. At a given point P, it is closest from the sun at a distance d₁ and has a speed v₁. At another point Q, when it is farthest from the sun at a distance d₂, its speed will be

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a

$\frac{d_{2}^{2} v_{1}}{d_{1}^{2}}$

b

$\frac{d_{2} v_{1}}{d_{1}}$

c

$\frac{d_{1}^{2} v_{1}}{d_{2}^{2}}$

d

$\frac{d_{1} v_{1}}{d_{2}}$

answer is C.

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Detailed Solution

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Angular momentum remains constant

${mv}_{1} d_{1} = {mv}_{2} d_{2} \Rightarrow v_{2} = \frac{v_{1} d_{1}}{d_{2}}$

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A planet moves around the sun. At a given point P, it is closest from the sun at a distance d1 and has a speed v1. At another point Q, when it is farthest from the sun at a distance d2, its speed will be