Question

Universal Law of gravitation is :

• A. $F = G \frac{Mm}{d^2}$
• B. $F = G \frac{m_1 m_2}{d^2}$
• C. $F = mg$
• D. 1 and 2 both

Hint:

Newton's Universal Law of Gravitation describes the attractive force between any two masses. The key is the product of the two masses and the inverse square of the distance between them, multiplied by the gravitational constant $G$. Different symbols for mass (e.g., $M, m$ or $m_1, m_2$) are equally valid.

Answer 1

The Correct Option is D

Step 1: Recall Newton's Universal Law of Gravitation.
Newton's Universal Law of Gravitation states that every particle attracts every other particle in the universe 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. Step 2: Express the law mathematically.
The mathematical formula for this law is typically written as: $F = G \frac{m_1 m_2}{r^2}$ or $F = G \frac{m_1 m_2}{d^2}$ where:
$F$ is the gravitational force between the two objects.
$G$ is the gravitational constant.
$m_1$ and $m_2$ are the masses of the two objects.
$r$ or $d$ is the distance between the centers of the two objects. Step 3: Analyze the given options.
Option (1) is $F = G \frac{Mm}{d^2}$. This formula uses $M$ and $m$ to represent the two masses, which is a common notation. So, this is a valid representation of the Universal Law of Gravitation.
Option (2) is $F = G \frac{m_1 m_2}{d^2}$. This formula uses $m_1$ and $m_2$ to represent the two masses, which is also a common notation. So, this is a valid representation of the Universal Law of Gravitation.
Option (3) is $F = mg$. This formula represents the weight of an object (the force of gravity on an object near a planet's surface), where $g$ is the acceleration due to gravity. This is a specific case derived from the Universal Law of Gravitation, but it is not the Universal Law itself. Step 4: Conclude which options are correct.
Both options (1) and (2) correctly represent the Universal Law of Gravitation, just using different variable names for the masses. Therefore, the correct answer is that both 1 and 2 are true. $$(4) 1 and 2 both$$