Suppose the earth increases its speed of rotation . At what new time period will the weight of a body on the equator becomes zero? Take `g=10 m/s^2` and radius of the earth `R=6400 km`.

Explanation

The weight will become zero when
`g' = 0 or g - R omega^(2)=0" "("on the equator" g' = g- R omega^(2))`
or `omega = sqrt((g)/(R))`
`:. (2pi)/(T)=sqrt((g)/(R))or T=2pisqrt((R)/(g))`
Substituting the values,
`T=(2pi sqrt((6400xx10^(3))/(10)))/(3600)"h" or T=1.4 "hr"`
Thus, the new time period should be 1.4 h instead of 24 h for weight of a body to be zero on the equator.