If the mass of earth is 80 times of that of a planet and...

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ' $\mathrm{g}$ ' on the earth is $9.8 \mathrm{~ms}^{-2}$, then the value of $\mathrm{g}^{\prime}$ on that planet is $=\ldots \ldots \ldots \mathrm{ms}^{-2}$ (A) $4.9$ (B) $0.98$ (C) $0.49$ (D) 49

Key Concepts

Newton's Law of Universal Gravitation

This law states that every two objects with mass attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It provides the fundamental basis for understanding gravitational interactions in both astronomical and terrestrial contexts.

Gravitational Acceleration Formula

The gravitational acceleration at the surface of a body is given by the formula g = GM/R², where G is the universal gravitational constant, M is the mass of the body, and R is its radius. This formula explains how gravity depends directly on mass and inversely on the square of the distance from the mass's center.

Scaling Relationships in Gravitational Systems

Scaling relationships help to understand how changes in a celestial body's mass and size affect its gravitational acceleration. If the mass of an object increases or if its radius changes, the gravitational acceleration on its surface changes proportionally—with mass increases leading to stronger gravity and increases in radius (which appear squared) leading to weaker gravity.

Ratio Comparison in Gravity Calculations

Using ratios to compare gravitational accelerations allows for simplification by canceling common factors. By comparing the mass and radius of two bodies using the formula g = GM/R², one can directly determine how changes in mass and diameter (or radius) affect the surface gravitational acceleration without needing to compute the exact value of the gravitational constant.

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