Understanding the Gravitational Constant (G)

The question asks for the value of the gravitational constant G, which appears in the formula for the force of attraction between two particles.

The force of attraction between two particles of masses \(m_1\) and \(m_2\) separated by a distance \(d\) is described by Newton's Law of Universal Gravitation. The formula given is:

\(F = \frac{Gm_1m_2}{d^2}\)

In this formula:

• \(F\) is the force of gravitational attraction between the two particles.
• \(m_1\) and \(m_2\) are the masses of the two particles.
• \(d\) is the distance between the centers of the two particles.
• \(G\) is the Universal Gravitational Constant.

The gravitational constant \(G\) is a fundamental physical constant that determines the strength of the gravitational force. Its value is experimentally determined.

The accepted value for the universal gravitational constant \(G\) is approximately \(6.674 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\). Looking at the options provided, we need to find the one that matches this value and its units.

Let's examine the options:

• Option 1: \(6.733 \times 10^{-17} \text{ Nm}^2 \text{kg}^2\). The exponent and the numerical value are incorrect, and the units are also incorrect (\(\text{kg}^2\) should be in the denominator).
• Option 2: \(6.6733 \times 10^{-17} \text{ Nm}^2 \text{kg}^2\). The exponent is incorrect, and the units are incorrect.
• Option 3: \(6.6733 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\). This numerical value (\(6.6733\)), exponent (\(-11\)), and units (\(\text{Nm}^2/\text{kg}^2\)) closely match the accepted value of the gravitational constant \(G\).
• Option 4: \(6.733 \times 10^{-11} \text{ Nm}^2 \text{kg}^2\). The numerical value is slightly different from the more commonly used one, and the units are incorrect.

Based on the standard value of the universal gravitational constant \(G\), option 3 provides the correct value and units.

The universal gravitational constant \(G\) has the value of approximately \(6.6733 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\).