Question

The effect of rotation of the Earth on the value of acceleration due to gravity is

• A. Maximum at both poles
• B. Minimum at both poles
• C. Maximum at equator and minimum at the poles
• D. Minimum at the equator and maximum at the poles

Answer 1

Answer: (C)

Maximum at equator and minimum at the poles

Answer 2

The variation in acceleration due to gravity due to the rotation of the Earth is given as
$g^{'}=g-\omega ^{2} \, Rcos^{2} \theta$ , Where

• g' = Change in the acceleration due to gravity
• g= Acceleration due to gravity on the surface of the earth
• R = Radius of the earth
• $\omega$ = Angular velocity of the earth
• $\theta$ = Lattitude

(i) At poles, $\theta =90^{ \, }$

$g_{p o l e}=g-\omega ^{2} \, Rcos^{2} 90^\circ =g-0$
$g_{pole}=g$

There is no effect (minimum effect) of the rotation of the earth on acceleration due to gravity at the poles.

(ii) At equator, $\theta =0^{ \, }$

$g_{e q u a t o r}=g-\omega ^{2} \, Rcos^{2} 0^\circ$
$g_{equator}= \, g-\omega ^{2} \, R$

The effect of the rotation of the Earth on acceleration due to gravity is maximum at the equator. The value of acceleration due to gravity is reduced by a factor of $\omega^2R$ at the equator.

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