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Which of the following constant values given in the options is equal to the universal gravitational constant 'G'?

$9.1 \times 10^{-31} \text{ kg}$

$9.8 \text{ ms}^{-2}$

$6.7 \times 10^{-11} \text{ Nm}^2 \text{kg}^{-2}$

$1.6 \times 10^{-19} \text{ C}$

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePrevious Year Paper 2024

Option C

$6.7 \times 10^{-11} \text{ Nm}^2 \text{kg}^{-2}$

Quick Summary:

The universal gravitational constant, denoted by ' $G$ ', is a physical constant that appears in Newton's law of universal gravitation. Its value is approximately $6.67 \times 10^{-11} \text{ Nm}^2\text{kg}^{-2}$ .

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🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of $G$ as the 'strength' or the 'volume dial' of gravity; even though gravity seems weak when you jump, it is this constant that keeps planets in orbit around the Sun and you standing firmly on the Earth.

🧠 Memory Mnemonic / Shortcut Aid

Remember the exponent: Gravity is weak, so it needs a very tiny 'negative' power, ' $10^{-11}$ ', to describe the force between everyday objects.

🔢 Key Formulas

$F = G \frac{m_1 m_2}{r^2}$ — Newton's law of universal gravitation

$G \approx 6.674 \times 10^{-11} \text{ Nm}^2\text{kg}^{-2}$ — The standard value of the gravitational constant

⚙️ Working Principle

According to Newton's law of universal gravitation, the force of attraction between two point masses $m_1$ and $m_2$ separated by a distance $r$ is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The proportionality constant $G$ allows us to equate these variables in the equation $F = G \frac{m_1 m_2}{r^2}$ .

📌 Key Points

▸
The constant $G$ is universal, meaning it remains the same everywhere in the universe.
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It is different from $g$ (acceleration due to gravity), which is approximately $9.8 \text{ ms}^{-2}$ on Earth.
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The unit is derived from the formula: $[G] = \frac{[F][r^2]}{[m_1][m_2]} = \frac{\text{N} \cdot \text{m}^2}{\text{kg}^2} = \text{Nm}^2\text{kg}^{-2}$ .

✅ Advantages

▸
Allows for precise calculation of planetary orbits and celestial mechanics.

❌ Disadvantages / Limitations

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Extremely difficult to measure accurately in a laboratory setting due to the weakness of gravitational force compared to other fundamental forces.

🛠️ Applications / Uses

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Calculating the mass of planets and stars.
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Predicting the trajectories of satellites and space probes.

📄 Additional Information

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Option A ( $9.1 \times 10^{-31} \text{ kg}$ ) is the mass of an electron.
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Option B ( $9.8 \text{ ms}^{-2}$ ) is the acceleration due to gravity on Earth ( $g$ ).
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Option D ( $1.6 \times 10^{-19} \text{ C}$ ) is the elementary charge of a proton or electron.

✅

C is correct — The value $6.7 \times 10^{-11} \text{ Nm}^2\text{kg}^{-2}$ corresponds to the universal gravitational constant ' $G$ '.

Core Concepts Used

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Universal Gravitation Fundamental Constants Newtonian Mechanics

💡 EXAM TIP

Don't confuse ' $G$ ' (Universal Gravitational Constant) with ' $g$ ' (Acceleration due to gravity). ' $G$ ' is the same everywhere, but ' $g$ ' changes based on the mass and radius of the planet you are on!

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