Thank you for reporting, we will resolve it shortly
Q.
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.
$ 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 $
$\therefore T _2^2=\frac{ T _1^2}{64}$
$\therefore T _2=\frac{24}{8}=3$