According to the Universal Law of Gravitation, if the distance between two objects is doubled, the gravitation

Question

According to the Universal Law of Gravitation, if the distance between two objects is doubled, the gravitational force between them becomes:

Examoogle · Accepted Answer

The correct answer is Option C: One-fourth of the original. According to Newton's Universal Law of Gravitation, the force of attraction between two bodies is inversely proportional to the square of the distance between their centers. When the distance is doubled ($2r$), the force becomes $\frac{1}{(2)^2} = \frac{1}{4}$ of its initial value.

Step-by-Step Solution & Concepts:
According to Newton's Universal Law of Gravitation, the force of attraction between two bodies is inversely proportional to the square of the distance between their centers. When the distance is doubled ($2r$), the force becomes $\frac{1}{(2)^2} = \frac{1}{4}$ of its initial value.

Working Principle: The gravitational force $F$ between two masses $m_1$ and $m_2$ separated by a distance $r$ is given by $F = G \frac{m_1 m_2}{r^2}$. If the new distance $r' = 2r$, then the new force $F' = G \frac{m_1 m_2}{(2r)^2} = G \frac{m_1 m_2}{4r^2} = \frac{1}{4} F$. This inverse-square relationship demonstrates that gravity rapidly weakens as objects move further apart.

Key Formulas: $F = G \frac{m_1 m_2}{r^2}$ — Newton's Law of Universal Gravitation; $F \propto \frac{1}{r^2}$ — Inverse Square Law relationship

Key Points: Gravitational force is directly proportional to the product of the masses.; Gravitational force is inversely proportional to the square of the distance between centers.; The constant $G$ is the Universal Gravitational Constant, approximately $6.674 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$.

Advantages: Explains planetary orbits and satellite motion accurately.

Disadvantages: Does not account for relativistic effects in extreme gravity (General Relativity is required there).

Applications: Calculation of orbital mechanics for satellites.; Predicting the behavior of tides influenced by the Moon.

Additional Info: The inverse square law is a fundamental characteristic of various physical forces, including electrostatics and light intensity.. Option A is incorrect because gravity is attractive and weakens with distance; Option B suggests an inverse linear relationship (which is incorrect); Option D would only happen if the distance were halved.

Answer: C is correct — Gravitational force follows the inverse square law, meaning doubling the distance results in the force becoming one-fourth of its original strength.

Exam Tip: Always verify if a law follows an inverse square or inverse linear relationship in physics exams; most field forces (Gravity, Electrostatics) follow the inverse square law.

Examoogle · Answer

Option A: Double the original

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Option B: Half the original

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Option D: Four times the original

Correct Answer

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