First slide

Motion of planets and satellites

Question

Two satellites of masses m₁ and m₂ (m₁ > m₂)are revolving around the earth in a circular orbit of radii r₁ and r₂(r₁ > r₂),respectively. Which of the following statements is true regarding their speeds v₁ and v₂?

Moderate

A

$v_{1} = v_{2}$
B

$v_{1} > v_{2}$
C

$v_{1} < v_{2}$
D

$\frac{v_{1}}{r_{1}} = \frac{v_{2}}{v_{2}}$

Solution

$\begin{array}{l} \frac{m_{1} v_{1}^{2}}{r_{1}} = m_{1} \frac{GM}{r_{1}^{2}}, \frac{m_{2} v_{2}^{2}}{r_{2}} = m_{2} \frac{GM}{r_{2}^{2}} \\ \frac{v_{1}^{2}}{v_{2}^{2}} = \frac{r_{2}}{r_{1}}; r_{2} < r_{1} \Rightarrow v_{1}^{2} < v_{2}^{2} \end{array}$
$Hence, v_{1} < v_{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App