Question

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

• A. 4 hours
• B. 6 hours
• C. 12 hours
• D. 3 hours

Answer 1

Answer: (D)

$T^2\propto R^3$
$\frac{T_1^2}{T_2^2}=\frac{R_1^3}{R_2^3}\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R}{\frac{R}{4}}\right)}^3$
$\therefore \frac{T_1^2}{T_2^2}=64$
$\therefore T_2^2=\frac{T_1^2}{64}$
$\therefore T_2=\frac{24}{8}=3$