Question

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become

• A. 10 hours
• B. 80 hours
• C. 40 hours
• D. 20 hours

Answer 1

Answer: (C)

Time period of a satellite $T=\frac{2\pi }{R_e}=\sqrt{\frac{r^3}{g}}$
$r=$ distance between satellite and the earth.
$T\propto r^{3/2}$
$\Rightarrow \frac{T_1}{T_2}={\left(\frac{r_1}{r_2}\right)}^{3/2}$
$T_2=8T_1=8\times 5=40$ hours