What is the time period of ratation of the earth around its axis so that the objects at the equator becomes weightless ? (g = 9.8 m//s^(2), Radius of earth= 6400 km)

What is the time period of ratation of the earth around its axis so th

1.	What is the time period of ratation of the earth around its axis so that the objects at the equator becomes weightless ? (g = 9.8 m//s^(2), Radius of earth= 6400 km)
Answer» Solution :G at the equator is `g_(0) = g-g_(0) = g - R omega^(2)` If bodies are to BECOME WEIGHTLESS at the equator, `g_(0) = 0`. `0 = g - R omega^(2) rArr R omega^(2) = g""omega = sqrt((g)/(R))` Time period of rotation, `T = (2pi)/(omega) = 2pi sqrt((R)/(g))` `R = 6400 xx 10^(3)m, g = 9.8 m//s^(2)` `T = 2pi sqrt((6.4 xx 10^(6))/(9.8)) = 5078 s = 84` minute 38s.