Correct Option
The correct option is (a).
Explanation
Newton's Law of Universal Gravitation describes the gravitational attraction between any two bodies with mass. It provides the mathematical relationship governing the force of attraction based on mass and distance.
Statement-wise Analysis
- Statement 1 is Correct: According to the law, the gravitational force ($F$) between two objects is directly proportional to the product of their masses ($m_1$ and $m_2$). Mathematically, $F \propto m_1 m_2$.
- Statement 2 is Incorrect: The law states that the force is inversely proportional to the square of the distance ($r$) between the objects ($F \propto \frac{1}{r^2}$), not linearly inversely proportional to the distance. This is a specific characteristic known as the inverse-square law.
- Statement 3 is Incorrect: Gravitational force is a central force. It acts along the line joining the centers of the two interacting objects. It does not act perpendicular to this line.
Key Takeaway: The Universal Law of Gravitation is represented by the formula $F = G \frac{m_1 m_2}{r^2}$. It is an attractive, central force that obeys the inverse-square law regarding distance.