Chapter 9, Problem 1RCQ

To determine

Newton’s discovery about gravity.

Answer to Problem 1RCQ

Solution: All material bodies in the universe attract each other and heavenly bodies also attract each by same nature of force.

Explanation of Solution

Two bodies attract each other in this universe and magnitude of the force is directly proportional to the product of mass of two bodies and inversely proportional to the square of distance between them.

Le.

$F$ : Gravitational force.

$m_1$ : Mass of one bod.

$m_2$ : Mass of other bod.

Then.

$F\propto m_1\times m_2$.........(1)

$F\propto \frac{1}{r^2}$.........(2)

From equation (1) and (2).

  $F\propto \frac{m_1\times m_2}{r^2}$

Apply constant G to get equality sign.

  $F=G\frac{m_1\times m_2}{r^2}$

$G$ : Gravitational constant

It always acts along the line joining the object and attractive in nature.

When Newton saw an apple fell from the tree on the Earth then he started to observe the motion of the heavenly body (Moon) around the Earth.This sparked the idea that the Earth attracts all bodies towards its center.

• By comparing the acceleration of apple and Moon :$F\propto \frac{1}{r^2}$

• By applying Newton’s third law of motion,

  $F\propto m_1\times m_2$

Conclusion:

Everything in the universe attracts each other and governed by simple law.