Question

The value of ‘g’ at a particular point is $9.8m/{s^2}$ suppose the earth suddenly shrinks uniformly to half its present size without any mass. The value of ‘g’ at the same point (assuming that the distance of the point from the center of earth does not shrink) will now be
(A). $4.9m/{s^2}$
(B). $3.1m/{s^2}$
(C). $9.8m/{s^2}$
(D). $19.6m/{s^2}$

Answer 1

Hint: In this question we will study the value of ‘g’ and give the reason why earth suddenly shrinks uniformly to half. We will also get to know what will be the value of ‘g’ at the same point. And hence, by this information we will be easily approaching our answer.

Complete step-by-step answer:
Acceleration of the gravity is referred to as ‘g’ and on earth its value is $9.8m/{s^2}$. On the surface of the earth at sea level the acceleration of the gravity is $9.8m/{s^2}$. Value of ‘g’ depends upon the location. In the value of ‘g’ about the earth’s surface there are slight variations. Square of the distance is inversely proportional to the gravitational force. $9.8m/{s^2}$ Is the numerical value of acceleration of gravity. Effects of tides are inversely proportional to the cube of the distance. Earth’s and moon’s distance between them is smaller than the distance between earth and the sun. On the earth’s tidal waves, the moon will have greater influence.
Thus, the formula for acceleration of gravitation is,
$ \Rightarrow a = \dfrac{{GM}}{{{R^2}}}$
Where,
Mass of the earth is ‘M’ and the separation between both masses is R. Keeping separation between them and mass the same volume may be reduced. Acceleration of gravity will remain constant; it is clear from the formula. If the earth shrinks suddenly uniformly the value of ‘g’ at the same point will be $9.8m/{s^2}$.
So, the value of ‘g’ will be $9.8m/{s^2}$ .
Hence, the correct option is (C) - $9.8m/{s^2}$

Note: The force of gravity on an object is smaller at the equator as compared to the poles. There is about 0.18% gravitational acceleration which alone causes this effect which is less at the equator than the poles.