Question

What will be the formula of mass of the earth in terms of g, R and G ?

• A. $G \frac{R}{g}$
• B. $g \frac{R^2}{G}$
• C. $g^2\frac{R}{g}$
• D. $G \frac{g}{R}$

Answer 1

The Correct Option is B

To determine the formula for the mass of the Earth in terms of gravitational acceleration g, radius of Earth R, and the gravitational constant G, we start by understanding the relationship between these variables through Newton's law of universal gravitation and the formula for gravitational acceleration at the surface of the Earth.

Newton's law of universal gravitation states:

F = \frac{G \cdot M \cdot m}{R^2}

where:

• F is the gravitational force between the Earth and an object of mass m
• G is the universal gravitational constant
• M is the mass of the Earth
• R is the radius of the Earth

The gravitational force F at the surface of Earth is also represented as F = m \cdot g, where g is the acceleration due to gravity. Equating the two expressions for F, we have:

m \cdot g = \frac{G \cdot M \cdot m}{R^2}

Dividing both sides by m and multiplying through by R^2, we solve for M:

g = \frac{G \cdot M}{R^2}

From this, isolating M gives:

M = \frac{g \cdot R^2}{G}

Thus, the formula for the mass of the Earth in terms of g, R, and G is g \frac{R^2}{G}.

Therefore, the correct answer is:

g \frac{R^2}{G}