Calculate the value of acceleration due to gravity at a place of lititude `30^(@)`. Radius of the Earth `6.4xx 10^(6)m`.The value of acceleration due to gravity on Earth is `9.8 m//s^(2)`.

Explanation

Here, `lambda = 30^(@), R = 6.4 xx 10^(6) m, g = 9.8 m//s^(2)`
`omega = (2pi)/(T) = (2xx (22//7))/(24 xx 60 xx 60) = 7.27 xx 10^(-5) rad//s`
Acceleration due to gravity at a place of lititude `lambda` is
`g' = g- R omega^(2) cos^(2) lambda`
`= 9.8 - (6.4 xx 10^(6)) xx (7.27 xx 10^(-5))^(2) xx cos^(2) 30^(@)`
`= 9.8 - 6.4 xx 7.27 xx 7.27 xx 10^(-4) xx (3//4)`
`= 9.8 - 0.025 = 9.775 ms^(-2)`