What happens with the force of gravitation between two objects when the mass of one object is doubled?
The force of gravitation is doubled
Understanding Gravitational Force and Mass
The force of gravitation is a fundamental force that exists between any two objects with mass. This force is always attractive and depends on several factors as described by Newton's Law of Universal Gravitation.
Newton's Law of Universal Gravitation
According to Newton's Law of Universal Gravitation, the force of gravitation ($F$) between two objects 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:
\[F = G \frac{m_1 m_2}{r^2}\]
Where:
- \(F\) is the force of gravitation between the two objects.
- \(G\) is the gravitational constant (a universal constant).
- \(m_1\) is the mass of the first object.
- \(m_2\) is the mass of the second object.
- \(r\) is the distance between the centers of the two objects.
Effect of Doubling Mass on Gravitational Force
The question asks what happens to the force of gravitation when the mass of one object is doubled, assuming the mass of the other object and the distance between them remain constant.
Let the original masses be \(m_1\) and \(m_2\), and the distance be \(r\). The original force of gravitation is:
\[F_{\text{original}} = G \frac{m_1 m_2}{r^2}\]
Now, let's double the mass of one object. Let's assume the mass of the first object is doubled, so the new mass is \(m'_1 = 2m_1\). The mass of the second object remains \(m_2\), and the distance remains \(r\).
The new force of gravitation ($F_{\text{new}}$) will be:
\[F_{\text{new}} = G \frac{(2m_1) m_2}{r^2}\]
We can rewrite this expression by factoring out the constant '2':
\[F_{\text{new}} = 2 \times \left(G \frac{m_1 m_2}{r^2}\right)\]
Notice that the expression inside the parentheses is the formula for the original force, \(F_{\text{original}}\). Therefore, we can write:
\[F_{\text{new}} = 2 \times F_{\text{original}}\]
This shows that when the mass of one object is doubled, and other factors (the other mass and the distance) are kept constant, the force of gravitation between the two objects is also doubled.
Summary of Changes
| Factor | Change | Effect on Force (F ∝ m) |
|---|---|---|
| Mass \(m_1\) | Doubled (\(2m_1\)) | Force is multiplied by 2 |
| Mass \(m_2\) | Remains \(m_2\) | Force is multiplied by 1 (no change) |
| Distance \(r\) | Remains \(r\) | Force is multiplied by 1 (no change based on distance) |
| Constant \(G\) | Remains \(G\) | Force is multiplied by 1 (no change) |
Combining these effects, the new force is \(2 \times 1 \times 1 \times F_{\text{original}} = 2 F_{\text{original}}\).
Thus, the force of gravitation between the two objects is doubled.
Revision Table: Gravitational Force Factors
| Factor | Relationship with Gravitational Force ($F$) | Example: If factor is doubled (others constant) |
|---|---|---|
| Mass ($m_1$) | Directly Proportional ($F \propto m_1$) | Force is doubled |
| Mass ($m_2$) | Directly Proportional ($F \propto m_2$) | Force is doubled |
| Distance ($r$) | Inversely Proportional to square ($F \propto \frac{1}{r^2}$) | Force becomes one-fourth (\(\frac{1}{2^2}\)) |
Additional Information: Gravitation Concepts
- Universal Law: Newton's law is called 'universal' because it applies to any two objects with mass, anywhere in the universe.
- Nature of Force: Gravitational force is always attractive, pulling masses towards each other.
- Weakest Force: Gravitation is the weakest of the four fundamental forces (gravitational, electromagnetic, strong nuclear, weak nuclear), but it is significant because it acts over infinite distances and affects all objects with mass.
- Weight: Weight is the force of gravity acting on an object's mass, usually due to a large celestial body like Earth.
Important Questions from Physics
Two balls, A and B, are thrown simultaneously, a vertically upward with a speed of 20 m/s from the ground and B vertically downward from a height of 40 m with the same speed and along the same line of motion. At what points do the two balls collide by taking acceleration due to gravity as 9.8 m/s 2?
On the basis of which principle does soap clean surfaces?
Which one of the following devices is used to measure atmospheric pressure?
Which one of the following energy is stored in the links between the atoms?
Who among the following has explained the phenomenon of photoelectric effect?
