Question

Calculate angular velocity of earth so that acceleration due to gravity at 60° latitude becomes zero. (Radius of earth = 6400 km, gravitational acceleration at poles = 10 m/s², cos 60° = 0.5)

Options

• 7.8 x 10^-2 rad/s

• 0.5 x 10^-3 rad/s

• 1 x 10^-3 rad/s

• 2.5 x 10^-3 rad/s

Answer 1

2.5 x 10^-3 rad/s

Explanation:

`"g'" = "g" - omega^2  "R" cos^2 lambda, lambda = 60°`

`therefore 0 = 1 - omega^2 xx 6400 xx 10^3 xx 1/4`

`therefore omega^2 = 10^-4/16 Rightarrow omega = 10^-2/4`

`therefore omega = 2.5 xx 10^-3  "rad/s"`