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

Explanation

When earth is rotating the apparent weight of a body at the equator is given by
`W_(app)=mg-mR omega^(2)`
If bodies are weightless at the equator
`0=mg-mRomega^(2)impliesg=Romega^(2)`
`impliesomega=sqrt(g/R)`
Time period `T=(2pi)/(omega)=2pi sqrt(R/g)`
`T=2pisqrt((6.4xx10^(6))/9.8)=5078s=84` minute 38s