A planet moving along an elliptical orbit is closest to sun at a distance r₁ and farthest away at

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7.Gravitation

easy

A planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively, then the ratio $\frac{v_1}{v_2}$ is

A

$\frac{r_2}{r_1}$

B

$\left(\frac{r_2}{r_1}\right)^2$

C

$\frac{r_1}{r_2}$

D

$\left(\frac{r_1}{r_2}\right)^2$

(AIPMT-2011)

Solution

According to the Law of conservation of angular momentum

$m v_1 r_1=m v_2 r_2$

$v_1 r_1=v_2 r_2$

$\frac{v_1}{v_2}=\left(\frac{r_2}{r_1}\right)$

Standard 11

Physics

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