Which of the following is NOT correct ?
The accepted value of G is 6.673 × 10–13
Universal Law of Gravitation Explained
The universal law of gravitation, put forth by Sir Isaac Newton, describes the attractive force that exists between any two objects in the universe. This law is fundamental to understanding how celestial bodies interact and how objects fall towards the Earth. It states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The mathematical expression for the gravitational force (\(F\)) between two objects is given by:
$$ F = G \frac{m_1 m_2}{r^2} $$
Where:
- \(F\) is the gravitational force between the two objects.
- \(G\) is the universal gravitational constant.
- \(m_1\) and \(m_2\) are the masses of the two objects.
- \(r\) is the distance between the centers of the two objects.
Gravitation Force Proportionality Analysis
Let's analyze each statement to determine which one is NOT correct regarding the universal law of gravitation and the gravitational constant G.
- Statement 1: "According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses." This statement is correct. As per the formula \(F = G \frac{m_1 m_2}{r^2}\), the gravitational force \(F\) is directly proportional to the product of the masses (\(m_1 m_2\)). This means if the masses of the objects increase, the gravitational force between them also increases.
- Statement 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 is correct. The formula \(F = G \frac{m_1 m_2}{r^2}\) clearly shows that the gravitational force \(F\) is inversely proportional to the square of the distance (\(r^2\)) between the objects. This implies that as the distance between objects increases, the gravitational force rapidly decreases.
- Statement 3: "The accepted value of G is 6.673 × 10–13" This statement is NOT correct. The internationally accepted value for the universal gravitational constant (\(G\)) is approximately \(6.674 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\). The exponent \(10^{-13}\) in the given statement is incorrect; it should be \(10^{-11}\). This constant was first accurately measured by Henry Cavendish.
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Statement 4: "The SI unit of G is (Nm2)/kg2"
This statement is correct. We can derive the SI unit of G from the gravitational formula \(F = G \frac{m_1 m_2}{r^2}\). Rearranging the formula to solve for \(G\):
$$ G = \frac{F r^2}{m_1 m_2} $$
Substituting the SI units for each quantity, we have: Force (\(F\)) in Newtons (N), Distance (\(r\)) in meters (m), and Mass (\(m\)) in kilograms (kg).
Therefore, the SI unit of G is:
$$ \frac{\text{N} \cdot \text{m}^2}{\text{kg} \cdot \text{kg}} = \frac{\text{Nm}^2}{\text{kg}^2} $$
Correct Statement Identification
Based on the analysis, Statement 3 provides an incorrect value for the universal gravitational constant \(G\). The actual value of \(G\) is approximately \(6.674 \times 10^{-11} \text{ Nm}^2/\text{kg}^2\), not \(6.673 \times 10^{-13}\).
Important Questions from Universal law of gravitation
Which of the following is NOT correct ?
Three point masses each of mass m are placed at the three corners of an equilateral triangle of side x. Find the resultant force acting on any one particle at the corner.
The force of attraction (F) between two particles having masses m 1and m 2is given by _______. (If r is the distance between them and G is a universal constant)
- Which phenomenon, successfully explained by the universal law of gravitation, relies on the combined and differential gravitational attraction exerted by both the moon and the sun on the earth?
- The law of gravitation helped to prove that:
