A man of 50 kg is standing on the school play ground at Trichy. The latitude of Trichy is `10.8^(@)`.
With what mimimum angular speed the earth must rotate so that the magnitude of gravitational force is equal to the magnitude of centrifugal force that he experiences? (Radius of the earth is 6400 km and `g=10ms^(-2)`.

Explanation

Gravitational force `=F_g = mg`
`=50 xx10 = 500 N`
Minimum angular speed `omega =?`
If `F_g=F_c`
`500= m omega^2 R cos theta`
`omega_(" new ") = (500)/(50xx6400xx10^(3)xxcos 10.8)`
`=1.59xx10^(-6)`
`omega_(" new ")= 1.261xx10^(-3)` rad/s.