Question

One can easily weight the earth by calculating the mass of the earth by using the formula:
A. $\dfrac{g}{G}R_E^3$
B. $\dfrac{g}{G}R_E^2$
C. $\dfrac{G}{g}R_E^{}$
D. $\dfrac{G}{g}R_E^3$

Answer 1

Hint: The above can easily be solved by using the formula of Newton’s Law of Gravitation given by the formula
$F = \dfrac{{GMm}}{{R_E^2}}$
First, we need to put mg in place of F because the weight of a body is mg due to gravity. After that equating it we can easily determine the value of mass of the earth.

Complete step by step answer:
Given that,
Mass of earth = M
Gravitational force constant = G
Acceleration due to gravity = g
Radius of earth = ${R_E}$

We know that,
According to Newton’s law of gravitation, the force between two bodies is directly proportional to product of their masses and inversely proportional to the square of distance between them.
Therefore, we have
$F = \dfrac{{GMm}}{{R_E^2}}$
F = force exerted by the gravity

On substituting the value of F, we have
$mg = \dfrac{{GMm}}{{R_E^2}}$
On further solving we get,
$M = \dfrac{g}{G}R_E^2$
So, finally we conclude that the mass of earth can be easily determined using the above formula.
Therefore, the mass of the earth by using the formula is given by, $M = \dfrac{g}{G}R_E^2$

Hence, the correct answer is option (B).

Note: Remember the formula of force “F=mg” and take precautions during calculation. To find the weight on the moon, we divide the weight on earth by the earth's force of gravity, which is 9.81m/s2. This calculates the mass of the object. Once we have the object's mass, we can find the weight by multiplying it by the gravitational force, which it is subject to.