The moon's radius is 1 / 4 that of earth and its mass is 1 /...

The moon's radius is $1 / 4$ that of earth and its mass is $1 / 80$ times that of the earth. If g represents the acceleration due to gravity on the surface of earth, that on the surface of the moon is
(A) $g / 4$
(B) $\mathrm{g} / 5$
(c) $\mathrm{g} / 6$
(D) $\mathrm{g} / 8$

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Key Concepts

Newton's Law of Universal Gravitation

This law states that every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It is the foundation for understanding gravitational phenomena and is mathematically expressed as F = GM1M2/R^2. The acceleration due to gravity on a body’s surface can be derived from this law using g = GM/R^2, where M is the mass of the body and R is its radius.

Dependence of Gravitational Acceleration on Mass and Radius

Gravitational acceleration (g) on the surface of a celestial body increases with the mass of the body and decreases with the square of its radius. This concept shows that if the mass is reduced, g becomes smaller, and if the radius is reduced, g becomes larger by a factor related to the square of the change. This relationship is crucial for comparing the surface gravity of different objects like planets or moons by considering how changes in their masses and radii affect the gravitational pull experienced at their surfaces.

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