Question

The difference in the acceleration due to gravity at the pole and equator is ______.

(g = acceleration due to gravity, R = radius of the earth; θ = latitude, ω = angular velocity, cos0° = 1, cos90° = 0)

Options

• `(Romega^2)/g^2`

• Rω² cos²θ

• Rω²

• ωcos²θ

Answer 1

The difference in the acceleration due to gravity at the pole and equator is Rω².

Explanation:

The value of acceleration due to gravity due to the rotation of the Earth,

g' = g - ω²Rcos²λ

At poles, λ = 90°

∴ `g_p = g - omega^2Rcos^2 90^circ = g`

At equator, λ = 0°

∴ `g_e = g - omega^2Rcos^2 0^circ = g - omega^2R`

∴ `g_p - g_e = g - g + Romega^2 = Romega^2`