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

The Correct Option is A

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