The gravitational force between two objects of masses m1 and m2 is directly proportional to
m1 × m2
Gravitational Force Proportionality Explained
This question asks about the relationship between the gravitational force acting between two objects and their masses. To answer this, we need to recall Newton's Law of Universal Gravitation.
Newton's Law of Universal Gravitation
Newton's Law states that the gravitational force (\(F\)) between any two objects in the universe is directly proportional to the product of their masses (\(m_1\) and \(m_2\)) and inversely proportional to the square of the distance (\(r\)) between their centers. The formula is expressed as:
\( F = G \frac{m_1 m_2}{r^2} \)
Here, \(G\) represents the universal gravitational constant.
Understanding Proportionality to Masses
From the formula \( F = G \frac{m_1 m_2}{r^2} \), we can see how the force \(F\) changes with respect to the masses \(m_1\) and \(m_2\). If we keep the distance \(r\) and the gravitational constant \(G\) the same, the formula simplifies to:
\( F \propto m_1 m_2 \)
This means the gravitational force (\(F\)) is directly proportional to the product of the two masses (\(m_1 \times m_2\)).
Analyzing the Options
Let's examine the given options based on Newton's Law:
- Option 1: \( m_2 - m_1 \) - This represents the difference between the masses. The gravitational force is not directly proportional to the difference in masses.
- Option 2: \( m_1 \times m_2 \) - This represents the product of the masses. According to Newton's Law, the gravitational force is directly proportional to this product. This matches our analysis.
- Option 3: \( m_1 - m_2 \) - This also represents the difference between the masses, similar to option 1. The gravitational force is not directly proportional to the difference in masses.
- Option 4: \( m_1 / m_2 \) - This represents the ratio of the masses. The gravitational force is not directly proportional to the ratio of the masses.
Conclusion
Based on Newton's Law of Universal Gravitation, the gravitational force between two objects is directly proportional to the product of their masses (\(m_1 \times m_2\)).
Similar Questions
The force exerted by the earth on the moon is:
(Consider G=\(6 \times 10^{-11}Nm^2kg^{-2}\) ; mass of the earth M=\(6 \times 10^{24}\)kg; mass of the moon= \(8 \times 10^{22}\) kg, and distance between earth and moon is \(4 \times 10^{8}\) m).Which of the following statements is/are correct?
Statements:
I) The mass of an object is the same as its weight.
II) The mass of an object is not the same as its weight.
III) Mass is scalar quantity, whereas weight is vector quantity.
Which of the following statements is/are correct?
Statements:
I) The Gravitational force between two objects is independent of the distance of separation between two objects.
II) The Gravitational force between two objects is inversely proportional to the square of the distance of the separation between two objects.
III) The Gravitational force between two objects is directly proportional to the product of their masses.
When an object falls under gravity, the object experiences:
If the acceleration due to gravity of the earth is 6 times the acceleration due to gravity on the moon, which of the following statements is correct?
Energy possessed by a body by virtue of its position or configuration is:
- Which of the following statements is/are INCORRECT?
A. The value of G on the moon is equal to that on the earth.
B. $26.68 \times 10^{-11}$ N is the force of gravitation between two point masses of 2 kg and 2 kg kept 1 m apart.
C. Newton's law of gravitation is valid in the laboratory only.
D. Force is inversely proportional to the square of the distance between two bodies. - What will be the force of attraction between two bodies weighing 20 kg and 50 kg, respectively, with a distance of 2 metre between them?
Important Questions from Gravitation
The known forces of nature can be divided into four classes, viz., gravity, electromagnetism, weak nuclear force and strong nuclear force. With reference to them, which one of the following statements is not correct?
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