Question

Near earths surface, time period of a satellite is $4 h$. Find its time period at height $4R$ from the centre of earth :

• A. $32\,h$
• B. $\left( \frac{1}{8\sqrt[3]{2}} \right)h$
• C. $8\sqrt[3]{2}$
• D. $16\,h$

Answer 1

Answer: (A)

$32\,h$

Answer 2

We know, $T^{2} \propto R^{3}$ $\therefore\left(\frac{T_{2}}{T_{1}}\right)^{2}=\left(\frac{R_{2}}{R_{1}}\right)^{3}$ $\Rightarrow \frac{T_{2}}{4}=\left(\frac{4 R}{R}\right)^{3 / 2}$ $\Rightarrow T_{2}=4 \times 8=32 \,h$