Question

Question 23
How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

Answer 1

The weight of the body decreases as the mass moves away from the earth as the distance between them grow. Acceleration due to gravity depends on the distance between the earth and body and if it increases the acceleration of the gravity due to earth on the body will decrease. Hence, the weight of the body will decrease if the body moves away from the earth.

If the diameter of the earth decreases to half, then the radius will also become half.

$F=\frac{GMm}{r^2}$

F(new weight of the body) $=G\times 4\times M\times \frac{m}{{\left(\frac{r}{2}\right)}^2}$

$=G\times 4\times 4\times M\times \frac{M}{r^2}$

New weight of the body $=16\times \left(\frac{GMm}{r^2}\right)$

=16 times (old weight of the body).