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

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

1.	What is the time period of rotation of the earth around its axis so that the objects at the equator becomes weightless ? (g=9.8m//s^2, Radius of earth = 6400 km)
Answer» Solution :g at the equator is `g_(0) = g -g_0 = g - Romega^2` If bodies are to become WEIGHTLESS at the equator , `g_(0)=0` `0 = g - Romega^2implies Romega^2=g` `omega=sqrt(g/R)` Time PERIOD of ROTATION , `T = (2pi)/omega=2pisqrt(R/g)` ` R= 6400 xx10^3 m, "" g = 9.8 m//s^2` `T = 2pisqrt((6.4xx10^(6))/(9.8))=5078s=84` minute 38s.