Answer:
[tex]3.59\times 10^{7}\ m[/tex]
Explanation:
r = Distance from the surface
T = Time period = 24 h
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
m = Mass of the Earth = 5.98 × 10²⁴ kg
From Kepler's law which balances centripetal force and the force of gravity we have relation
[tex]T^2=\dfrac{4\pi^2r^3}{GM}\\\Rightarrow r=\dfrac{T^2GM}{4\pi^2}\\\Rightarrow r=\left(\dfrac{(24\times 3600)^2\times 6.67\times 10^{-11}\times 5.98\times 10^{24}}{4\pi^2}\right)^{\frac{1}{3}}\\\Rightarrow r=42250474.30504\ m[/tex]
Distance from the center of the Earth would be
[tex]42250474.30504-6.38\times 10^6=35870474.30504\ m=3.59\times 10^{7}\ m[/tex]
