What is the SI unit of universal gravitational constant $ G $? | General Science MCQ | Examoogle

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What is the SI unit of universal gravitational constant $G$ ?

$N m^2 / kg^{-1}$

$N m^2 / kg s^{-1}$

$N kg m^2$

$N m^2 / kg^2$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option D

$N m^2 / kg^2$

Quick Summary:

The Universal Gravitational Constant $G$ is a fundamental constant used in Newton's Law of Universal Gravitation. Its SI unit is derived from the formula for gravitational force, which is $F = G \frac{m_1 m_2}{r^2}$ . By rearranging to solve for $G$ , we get $G = \frac{F r^2}{m_1 m_2}$ , leading to the unit $\text{N m}^2 \text{kg}^{-2}$ or $\text{N m}^2 / \text{kg}^2$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Just as a 'scale factor' helps convert between different units like inches and centimeters, $G$ acts as the scaling factor that translates how much 'stuff' (mass) and 'space' (distance) exists between two objects into the physical 'tug' (force) felt between them.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'Newt-meter-squared, kilograms-squared' (NM2-KG2) to keep the units straight: $N \cdot m^2 / kg^2$ .

🔢 Key Formulas

$F = G \frac{m_1 m_2}{r^2}$ — Newton's Law of Universal Gravitation

$G = \frac{F \cdot r^2}{m_1 \cdot m_2}$ — Dimensional derivation of the gravitational constant unit

⚙️ Working Principle

According to Newton's law, the gravitational force $F$ between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The constant $G$ acts as a proportionality constant, ensuring the unit consistency between force (Newtons), distance (meters), and mass (kilograms).

📌 Key Points

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The numerical value of $G$ is approximately $6.674 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ .
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It is a scalar quantity, not a vector.
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It is distinct from the acceleration due to gravity, $g$ , which is locally dependent on planetary mass and radius.

✅ Advantages

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Allows for the calculation of gravitational forces between any two objects in the universe.

❌ Disadvantages / Limitations

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It is extremely difficult to measure precisely in laboratory settings due to the minuscule strength of gravitational force compared to other fundamental forces.

🛠️ Applications / Uses

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Calculating the orbital paths of planets and satellites.
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Determining the mass of celestial bodies like stars and planets.

📄 Additional Information

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The unit $N m^2 / kg^2$ is dimensionally equivalent to $m^3 kg^{-1} s^{-2}$ .
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Option D represents the correct SI unit notation ( $N m^2 / kg^2$ ).

📊 Diagram / Illustration

✅

D is correct — The SI unit of the Universal Gravitational constant $G$ is $\text{N m}^2 \text{kg}^{-2}$ , which is commonly written as $\text{N m}^2 / \text{kg}^2$ .

Core Concepts Used

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Newton's Law of Universal Gravitation SI Units Dimensional Analysis Fundamental Constants

💡 EXAM TIP

Always perform dimensional analysis if you forget a constant's unit; start with the defining equation ( $F=ma$ or $F=GmM/r^2$ ) and substitute the base units.

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