First slide

Motion of planets and satellites

Question

Two satellites A and B of masses $m_{1} and m_{2} (m_{1} = 2 m_{2})$ are moving in circular orbits of radii $r_{1} and r_{2} (r_{1} = 4 r_{2})$ , respectively, around the earth. If their periods are T_A and T_B, then the ratio T_A/T_B is

Moderate

A

4
B

16
C

2
D

8

Solution

$\begin{array}{l} m_{1} = 2 m_{2} \Rightarrow \frac{m_{1}}{m_{2}} = 2 \\ r_{1} = 4 r_{2} \Rightarrow \frac{r_{1}}{r_{2}} = 4 \\ T_{A}^{2} \propto r_{1}^{2} and T_{B}^{2} \propto r_{2}^{3} \\ \Rightarrow \frac{T_{A}}{T_{B}} = 8 \end{array}$

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