Question

A planet is revolving around the sun in an elliptical orbit. its closets distance from the sun is $r_{min}$. The farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is nearest to the sun is $\omega$, then the orbital angular velocity at the point when it is at the farthest distance from the sun is

• A. $\sqrt{\left(r_{min}/r_{max}\right)}\omega$
• B. $\sqrt{\left(r_{max}/r_{min}\right)}\omega$
• C. $\left(r_{ma{x}^2}/r_{mi{n}^2}\right)\omega$
• D. $\left(r_{mi{n}^2}/r_{ma{x}^2}\right)\omega$

Answer 1

The correct option is D $\left(r_{mi{n}^2}/r_{ma{x}^2}\right)\omega$

$v_1{r}_1=v_2{r}_2$ or $r_1^2{\omega }_1=r_2^2{\omega }_2$
($\because L=mrv=constant$)
or $r_{mi{n}^2}\omega =r_{ma{x}^2}{\omega }^{\prime }$
$\therefore {\omega }^{\prime }=\left(r_{min}^2/r_{max}^2\right)\omega$