Q.How is the gravitational force between two point masses affected when they are dipped in water keeping the separation between them the same?

The key idea is that the gravitational force between two masses is a fundamental interaction that depends only on their masses and the distance between them, not on the intervening medium.

Newton's Law of Universal Gravitation states that the force $F$ between two point masses $m_1$ and $m_2$ separated by a distance $r$ is given by $F = G \frac{m_1 m_2}{r^2}$. …

The gravitational force is one of the fundamental forces of nature, describing the attraction between any two objects with mass. Understanding how this force behaves in different environments requires looking at its fundamental definition.

The key concept here is Newton's Law of Universal Gravitation, which states that every particle in the universe attracts every other particle 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. Crucially, this law involves a constant, $G$, which is a universal constant.

Unlike forces like the electrostatic force, which depends on the permittivity of the medium (often expressed through a dielectric constant), the gravitational force is not mediated by the surrounding material. It is an intrinsic interaction between masses themselves.

1. Recall Newton's Law of Universal Gravitation:

   The magnitude of the gravitational force ($F_g$) between two point masses, $m_1$ and $m_2$, separated by a distance $r$, is given by the formula:

   $F_g = G \frac{m_1 m_2}{r^2}$

   Here, $G$ is the universal gravitational constant.

2. Analyze the components of the formula:

   • $m_1$ and $m_2$: These are the masses of the two point objects.
   • $r$: This is the distance between the centers of the two point objects.
   • $G$: This is the universal gravitational constant, approximately $6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2$.

3. Consider the effect of dipping in water:

   • Masses ($m_1, m_2$): When the two point masses are dipped in water, their intrinsic masses do not change. Mass is a fundamental property of an object and is independent of the surrounding medium.
   • Separation ($r$): The problem statement explicitly says that the separation between them is kept the same. So, $r$ remains constant. …

Step 1: Newton's law F=G m1 m2/r^2 depends only on the two masses, separation, and G. Step 2: G is a true constant of nature; unlike electrostatics, gravity has no medium-dependence term. Step 3: immersing the masses in water leaves m1, m2, r, and G …