What should be the angular velocity of earth, if the apparent value of acceleration due to gravity at earth's surface on equatorial plane is zero ? Radius of earth is 6400 km and g at earth's surface is `10m//s^(2)`.

Options

A. 125 rad/s
B. 1.25 rad/s
C. `1.25xx10^(-3)"rad/s"`
D. zero

Answer

c

Explanation

`Mromega^(2)=mg`
`omega^(2)=(g)/(R)`
`omega=sqrt((10)/(0.4xx10^(6)))`
`=(10)/(8)xx10^(-3)=1.25xx10^(-3)" rad/s"`