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.
$T\propto r^{3/ 2}$
$\Rightarrow \frac{T_{1}}{T_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{3/ 2}$
$T_{2} = 8T_{1} = 8 × 5 = 40$ hours