Question

If the earth stops rotating about its own axis then what will be the change in the value of g at a place.
1) on the equator
2)on the pole
Radius of the earth = 6.4 $\times {10}^6$ m

Answer 1

Without rotation, Earth will not have an equatorial bulge and its radius will go to its average radius of $6,371km$. The simplest way to get this answer is to use the notion of centrifugal force. When a body rotates about the center of the Earth, the action of inertia shows up as if an apparent centrifugal force is acting upon it pointing away from the center of the Earth in effect canceling a very small part of the weight. The magnitude of that force is $\frac{m{v}^2}{R}sotheaccelerationcorrespondingtoitis$\dfrac{v^2}{R}.

Average Radius of Earth $=R=6,371,000m$

Earth period $=T=24hours=24\times 3600s=86400s$

Equatorial velocity $=V=\frac{2\left(3.1416\right)R}{T}=2\times 3.1416\times \frac{6,371,000}{86400}m/s$

$=463.3m/s$

Centripetal Acceleration $=g_1=\frac{V^2}{R}=\frac{\left({463.3}^2\right)}{6,371,000}$

$=0.0337m/s^2$

The equatorial g will increase by amount g1 when not rotating and will be equal to polar g.