Basic physics circular motion question?

There're two forces acting on the object at the equator, its weight mg and the normal force Fn exerted by the ground. The weight force acts toward the center of the planet, while the normal force acts in the opposite direction. The net force is called the centripetal force and must point toward the center. We use Newton's second law F = mg – Fn = ma = mv²/r. Zero apparent weight means there's no contact force between the ground and the object (Fn = 0), the object does not exert any force on the ground (if we put the scale under it, it would read zero). So, mg – 0 = mv²/r or, after cancelling an m out, v = √(gr) = √(10 m/s² x 7.9 x 10^6 m) = 8,888 m/s. The rotational speed v = 2πr / T and T = 2πr / v = 2π x 7.9 x 10^6 m / 8,888 m/s = 5585 s = 1.6 h.