Question

The value of g at a particular point is $10m{s^{ - 2}}$. Suppose the earth shrinks uniformly to half of its present size without losing any mass. The value of g at the same point (assuming that the distance of the point from the centre of the earth does not change) will now be.
${\text{A}}{\text{. 5m}}{{\text{s}}^{{\text{ - 2}}}} \\\ {\text{B}}{\text{. 10m}}{{\text{s}}^{{\text{ - 2}}}} \\\ {\text{C}}{\text{. 3m}}{{\text{s}}^{{\text{ - 2}}}} \\\ {\text{D}}{\text{. 20m}}{{\text{s}}^{{\text{ - 2}}}} \\\$

Answer 1

Hint: To get the right answer to this problem we have to use the formula of acceleration due to gravity in terms of mass and distance from the center of the planet. We have to consider the mass as constant here.

Complete step-by-step answer:

We know that the formula of gravitational field due to earth at a distance R from the center is and mass M is

$g = \dfrac{{GM}}{{{R^2}}} = 10m{s^{ - 2}}$ (In case of earth)

When the earth shrinks its mass remains constant and the distance from the center also remains constant so the term

$g = \dfrac{{GM}}{{{R^2}}}$ also equals $10m{s^{ - 2}}$.

Hence we come to know that the acceleration due to gravity does not change if the mass of earth is constant but its size shrinks.

So, the right answer is $10m{s^{ - 2}}$.

The correct option is A.

Note: In such problems we need to understand the concept and think what will be changed and what does not then according to that we have to solve these problems in order to get the desired result. Here we just have taken the help of the formula $g = \dfrac{{GM}}{{{R^2}}}$ in which any of the quantities doesn’t change in shrinking the size of earth. Doing this will solve your problem and will give you the right answer.