Answer
$87.5\ min$
Work Step by Step
We know that velocity $v=\frac{Distance }{time}$.
In this case, distance is the circumference of the circle i,e $2\pi R$.
Therefore, the formula for velocity becomes:
$v = \frac{2\pi R}{T}$
Another formula for linear velocity is $v = \sqrt \frac{GM_e}{r}$
Equating above formulas, we can get:
$\frac{2\pi R}{T}= \sqrt \frac{GM_e}{r}$
$\frac{T}{2\pi R}=\sqrt \frac{r}{GM_e}$
$T =2\pi\sqrt \frac{r^3}{GM_e}$
$T =2\pi\sqrt \frac{(6.37\times 10^{6}+0.16\times 10^{6})^3}{(6.67\times 10^{-11})(5.98\times 10^{24})}$
$T = 5249.719\ sec$
$T =\frac{5249.719}{60}=87.5\ min$
