If M is mass of the earth and R its radius, the ratio of the...

If $M$ is mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is
(A) $\frac{R^{2}}{M}$
(B) $\frac{M}{R^{2}}$
(C) $M R^{2}$
(D) $\frac{M}{R}$

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Key Concepts

Newton's Law of Universal Gravitation

This law describes the gravitational force between two masses and forms the foundation for understanding gravitational interactions. It states that the force between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers, with the gravitational constant as the proportionality factor.

Gravitational Acceleration

Gravitational acceleration on the surface of a spherical body is defined as the acceleration due to the gravitational force exerted by the body on an object near its surface. It is derived using Newton's law of gravitation by considering the mass of the body and its radius, resulting in the expression g = GM/R², which relates the gravitational acceleration to the gravitational constant, the mass of the body, and its radius.

Ratio and Dimensional Analysis

Calculating ratios of physical quantities, such as dividing the gravitational acceleration by the gravitational constant, requires careful dimensional analysis to ensure the mathematical manipulation respects units. In this context, understanding the ratio helps isolate the dependence on mass and radius, independent of the gravitational constant's dimensional contribution.

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