Question

If the earth stops rotating suddenly, the value of g at any point other than the poles would be
A) decrease
B) constant
C) increase
D) increase or decrease depending on position of earth

Answer 1

Write down the effect due to rotation of earth on gravitational acceleration. Find the gravitational constant at poles where the angle is ninety degrees. Next, find out the gravitational acceleration at any point and compare it with the acceleration of gravity at the poles. We can easily know if it's increasing or decreasing.

Formula used:
${{g}_{p}}={{g}_{e}}-R{{\omega }^{2}}{{\cos }^{2}}\alpha$

Complete answer:
Effect of rotation of earth on the acceleration due to gravity is given by the formula ${{g}_{p}}={{g}_{e}}-R{{\omega }^{2}}{{\cos }^{2}}\alpha$ where R is the radius of the earth, $\omega$ is the angular velocity of the rotation of earth and p is any point or latitude.
Now, let’s calculate the effect of rotation of earth on acceleration of gravity at the poles. We know at poles,
$\begin{aligned} & \alpha ={{90}^{0}} \\\ & {{g}_{p}}={{g}_{e}}-R{{\omega }^{2}}{{\cos }^{2}}\alpha \\\ & {{g}_{p}}={{g}_{e}}=cons\tan t \\\ \end{aligned}$
Thus, as the earth stops rotating, the value of acceleration of gravity at any point p will increase by an amount of $R{{\omega }^{2}}{{\cos }^{2}}\alpha$ everywhere except the poles.

So, the correct answer is “Option C”.

Additional Information:
As we move from the equator to the poles, the distance of the point of surface of earth from the centre of earth decreases. Hence, the acceleration due to gravity increases. Variation in acceleration due to gravity will be accordingly changed. The acceleration of gravity is least at the equator and is maximum at the points of poles. The acceleration of gravity depends on mass of the body, distance from the centre of the earth and a constant G, called as the universal constant of gravitation.

Note:
The value of gravitational acceleration is minimum at equators and maximum at the poles of earth. It is maximum at both north pole and south pole. The gravitational acceleration at the equator is minimum because the force of gravity on an object is smaller at the equator compared to that of the poles.