Question

The time period of satellite of earth is $5$ hr. If the separation between earth and the satellite is increased to $4$ times the previous value, the new time period will become:

• A. $10hrs$
• B. $80hrs$
• C. $40hrs$
• D. $20hrs$

Answer 1

Answer: (C)

$40hrs$

Time period $T^2=\frac{4{\pi }^2}{GM}{R}^3$
i.e $T^2\propto R^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R_1}{R_2}\right)}^3$
Here, $\frac{R_1}{R_2}=\frac{R}{4R}$ ; assuming the separation is from earth's centre.
${\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R}{4R}\right)}^3=\frac{1}{64}$
$\Rightarrow T_2=T_1\times {64}^{1/2}=5\times 8=40$ hr