Question

Write the universal law of gravitation. Derive
the mathematical expression for the force acting
on the two bodies in the universe.

Answer 1

Answer:

Universal law of Gravitation or Newton's law of Gravitation :

Statement : It states that every body in the universe attracts every another body with a force. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let the two bodies be as P and Q.

• m₁ = Mass of body P
• m₂ = Mass of body Q
• r = Distance between P and Q.
• F = Force of attraction.

According to the statement :

$\longrightarrow\sf F \propto m_{1}m_{2} \: \: \: ...(i)$

Also,

$\longrightarrow\sf F \propto \dfrac{1}{ {r}^{2} } \: \: \: ...(ii)$

From equation (I) and (ii) we have:

$\longrightarrow\sf F \propto \dfrac{m_{1}m_{2}}{ {r}^{2} }$

• G is a constant of proportionality known as universal gravitational constant.

$\longrightarrow \gray{\underline{ \boxed{ \orange{\bold{ F = G. \dfrac{m_{1}m_{2}}{ {r}^{2} }}}}}}$