The time period a satellite of earth is 5 hours. If the separation between the earth and the satellite in…

The time period a satellite of earth is 5 hours. If the separation between the earth and the satellite in increased to four times the previous value, the new time period of the satellite will be
  1. 20 hours
  2. 40 hours
  3. 80 hours
  4. 10 hours

Solution

$\begin{aligned} & \mathrm{T}^2 \alpha \mathrm{r}^3 \\ & \therefore \frac{\mathrm{T}_2^2}{\mathrm{~T}_1^2}=\frac{\mathrm{r}_2^3}{\mathrm{r}_1^3}=(4)^3=64 \\ & \therefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=8 \text { or } \mathrm{T}_2=8 \mathrm{~T}_1=8 \times 5=40 \text { hours. }\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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