Range of the gravitational force is :

Question

Accepted Answer

The correct answer to the question about the range of the gravitational force is Option 2: Infinite. Here is a detailed explanation supporting this choice and why the other options are incorrect:

1. **Explanation for Option 2 (Infinite):**
   - Gravitational force is described by Newton's Law of Universal Gravitation, which states that every point mass attracts every other point mass in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is given by $ F = G \frac{m_1 m_2}{r^2} $, where $ G $ is the gravitational constant, $ m_1 $ and $ m_2 $ are the masses, and $ r $ is the distance between the centers of the two masses.
   - The key aspect of this formula is that there is no term that limits the distance $ r $ at which the force acts. This implies that the gravitational force extends over infinite distances, albeit becoming weaker as the distance increases. Therefore, the range of gravitational force is theoretically infinite, as it can act over any distance, no matter how large.

2. **Why the other options are incorrect:**
   - **Option 1 (10$^{-14}$ m):** This option suggests a very short range for gravitational force, which is incorrect. Gravitational force is not limited to such a minuscule range. It acts over vast distances, as evidenced by the gravitational interactions between celestial bodies like planets, stars, and galaxies.
   - **Option 3 (10$^{-15}$ m):** Similar to Option 1, this option proposes an extremely limited range for gravitational force. Such a short range is characteristic of forces like the strong nuclear force, not gravity. Gravity is a long-range force that can act over astronomical distances.
   - **Option 4 (1 m):** This option suggests that gravitational force is limited to a range of 1 meter, which is incorrect. Gravitational force is responsible for the orbits of planets around the sun and the binding of galaxies, indicating that it operates over much larger distances than 1 meter.

In conclusion, the gravitational force has an infinite range, as it can act over any distance, no matter how large, which is why Option 2 is the correct answer.