What is the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation.

42400 Km

$\omega^2 r=\frac{G M}{r^2} \Rightarrow r^3=\frac{G M}{\omega^2}$

$\Rightarrow r=\left(\frac{G M}{R_e^2} \frac{R_e^2}{\omega^2}\right)^{1 / 3} \Rightarrow r=\left(\frac{g^2}{\omega^2}\right)^{1 / 3}$

Putting  $\omega=\frac{2 \pi}{T}=\frac{2 \pi}{86400}$ rad/sec

R = 6.4 × 10⁶ m

g = 9.8 m/sec², we get r = 42400 Km (Approx)