A classical mechanics problem by A Former Brilliant Member

Orbital velocity, $V_o=\sqrt{ \frac{GM}{R}}$

Time Period, $T= \frac{2 \pi R}{V_o} = 2 \pi R/ \sqrt{ \frac{GM}{R}} = \frac{2 \pi}{ \sqrt{GM}} R^{ \frac{3}{2}}$

Or $T\ \alpha\ R^{ \frac{3}{2}}$

Given that $R_1 = 36000km;\ T_1=24 h;\ R_2 ~ 6400km;\ T_2=?$

$\frac{T_2}{T_1}= (\frac{R_2}{R_1})^{ \frac{3}{2}} \\ \\ \Rightarrow T_2 = 24 \times (\frac{6400}{36000})^{ \frac{3}{2}} \\ \\ \Rightarrow T_2 = 1.79 h$

Notice that I have taken $R_2$ as 6400km, but it is more than 6400km. Since time period is directly proportional to $R^{ \frac{3}{2}}$ , time period will be slightly higher than 1.79 h. So the answer is $\boxed{2h}$ .