Question

A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is $r$ and the farthest distance is $R$. If the velocity of the planet nearest to the sun be $v$ and that farthest away from the sun be $V$, then $v/V$ is :

• A. $R^2/r^2$
• B. $r^2/R^2$
• C. $R/r$
• D. $r/R$

Answer 1

The correct option is C $R/r$

As angular momentum is conserved, hence we have the equation:

$I_1{\omega }_1=I_2{\omega }_2$

For elliptical body, $I=M{r}^2.$

So,

$M{R}_1^2{\omega }_1=M{R}_1^2{\omega }_2$

$M{R}_1{v}_1=M{R}_2{v}_2$

(Since, $\omega =\frac{v}{R})$

So, $R_1{v}_1=R_2{v}_2$

i.e. $RV=vr$

$(Since,v_2=Vand{v}_1=v)$

$\frac{v}{V}=\frac{R}{r}$

Thus option C is correct.