The value of universal gravitational constant is __________.

Question

Examoogle · Accepted Answer

The correct answer is Option C: $6.7 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$. The universal gravitational constant, denoted as $G$, is a fundamental physical constant involved in the calculation of gravitational effects. Its accepted value is approximately $6.674 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$, which is typically rounded to $6.7 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ for most competitive exam calculations.

Step-by-Step Solution & Concepts:
The universal gravitational constant, denoted as $G$, is a fundamental physical constant involved in the calculation of gravitational effects. Its accepted value is approximately $6.674 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$, which is typically rounded to $6.7 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ for most competitive exam calculations.

Working Principle: According to Newton's law of universal gravitation, the force $F$ between two masses $m_1$ and $m_2$ separated by a distance $r$ is given by $F = G \frac{m_1 m_2}{r^2}$. The constant $G$ acts as the proportionality factor that defines the strength of the gravitational force in the universe. It was first accurately measured by Henry Cavendish using a torsion balance experiment.

Key Formulas: $F = G \frac{m_1 m_2}{r^2}$ — Newton's law of universal gravitation; $G \approx 6.67 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ — Standard value of the universal gravitational constant

Key Points: The constant $G$ is different from the acceleration due to gravity ($g$), where $g \approx 9.8 	ext{ m/s}^2$ on Earth.; The value of $G$ is constant throughout the universe and does not depend on the medium or the nature of the bodies.; The SI unit of $G$ is derived from the formula: $\frac{	ext{Force} 	imes 	ext{Distance}^2}{	ext{Mass}^2} = 	ext{N m}^2 	ext{ kg}^{-2}$.

Advantages: Allows prediction of planetary orbits and satellite trajectories.

Disadvantages: Extremely difficult to measure precisely due to the weakness of gravitational forces at laboratory scales.

Applications: Calculation of orbital mechanics for satellites and spacecraft.; Determination of the mass of celestial bodies like planets and stars.

Additional Info: The value $6.7 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$ is the standard scientific approximation used in physics problem-solving.. Options A, B, and D provide incorrect magnitudes or powers of ten that do not correspond to the physical reality of gravitational interaction.

Answer: C is correct — The universal gravitational constant $G$ is scientifically accepted as $6.7 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$.

Exam Tip: Do not confuse $G$ (Universal Gravitational Constant, same everywhere) with $g$ (Acceleration due to gravity, which varies with height, depth, and latitude).

Examoogle · Answer

Option A: $6.7 	ext{ N m}^2 	ext{ kg}^{-2}$

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Option B: $5 	imes 10^{-1} 	ext{ N m}^2 	ext{ kg}^{-2}$

Examoogle · Answer

Option D: $1 	imes 10^{-11} 	ext{ N m}^2 	ext{ kg}^{-2}$

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