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

The correct option is C $40$ hours

$T^2\propto R^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$
$\Rightarrow \left(\frac{T_1}{T_2}\right)={\left(\frac{R_1}{R_2}\right)}^{3/2}={\left(\frac{1}{4}\right)}^{3/2}$
$\Rightarrow \frac{T_2}{T_1}=(4{)}^{3/2}=8$
$\Rightarrow T_2=8\times T_1=8\times 5=40$ hours