Question

A planet revolves about the sun in elliptical orbit. The arial velocity $\left(\frac{ d A }{ dt }\right)$ of the planet is $4.0 \times 10^{16} m ^{2} / s$. The least distance between planet and the sun is $2 \times 10^{12} m$. Then the maximum speed of the planet in $km / s$ is:

• A. 10
• B. 20
• C. 40
• D. None of these

Answer 1

Answer: (C)

$\frac{ d A }{ dt }=\frac{ r ^{2} \omega}{2}$ is constant
$\therefore \frac{ d A }{ dt }=\frac{ r _{\max }^{2} \omega_{\min }}{2}=\frac{ r _{\min }^{2} \omega_{\max }}{2} $
$\Rightarrow \omega_{\min }=\frac{2 d A / dt }{ r _{\max }^{2}} $
$ V _{\max }=\omega_{\min } r _{\min }=\frac{2 d A / dt }{ r _{\min }}=40\, k m / s$