Universal Gravitation Law: Identifying Incorrect Statements

This question asks us to identify the incorrect statement regarding Newton's universal law of gravitation. Let's analyze each statement:

Understanding Newton's Law of Gravitation

Newton's universal law of gravitation describes the attractive force between any two objects with mass. The law states that this gravitational force is:

• Directly proportional to the product of the masses of the two objects. Mathematically, this can be represented as: $F \propto m_1 m_2$.
• Inversely proportional to the square of the distance between their centers. Mathematically: $F \propto \frac{1}{r^2}$, where $r$ is the distance between the centers of the objects.

Combining these, the force $F$ is given by the equation:

Where:

• $F$ is the gravitational force
• $m_1$ and $m_2$ are the masses of the two objects
• $r$ is the distance between the centers of the objects
• $G$ is the universal gravitational constant

Analyzing the Options

Let's examine each option based on the universal law of gravitation:

• Option 1: "According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses". This statement correctly describes the relationship between gravitational force and mass.
• Option 2: "According to the universal law of gravitation, the force between two objects is inversely proportional to the square of the distance between them." This statement correctly describes the inverse square relationship between gravitational force and distance.
• Option 3: "The accepted value of G is 6.673 × 10 ^–13". The universally accepted value for the gravitational constant G is approximately $6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$. The value presented in this option ($6.673 \times 10^{-13}$) is significantly different and therefore incorrect.
• Option 4: "The SI unit of G is (Nm ²)/kg ²". By rearranging the formula $F = G \frac{m_1 m_2}{r^2}$ to solve for G, we get $G = F \frac{r^2}{m_1 m_2}$. The SI units are Newtons (N) for force, kilograms (kg) for mass, and meters (m) for distance. Thus, the unit for G is $\text{N} \cdot \text{m}^2 / (\text{kg} \cdot \text{kg})$, which simplifies to $\text{N m}^2/\text{kg}^2$. This statement is correct.
• Option 5: This option is blank and does not present a statement.

Conclusion

Based on the analysis, the incorrect statement is Option 3 because the accepted value of the universal gravitational constant G is approximately $6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$, not $6.673 \times 10^{-13}$.