What is NEWTON'S LAW OF GRAVITATION - Concept with example.
NEWTON'S LAW OF GRAVITATION :
It states that every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.
Vector form of Newton's law of Gravitation :
let
Negative sign shows that :
(i) The direction of is opposite to that
(ii) The gravitational force is attractive in nature
The gravitational force between two bodies are equal in magnitude and opposite in direction.
Example :
1.Two particles of masses 1 kg and 2 kg are placed at a separation of 50 cm. Assuming that the only forces acting on the particles are their mutual gravitation, find the initial acceleration of heavier particle.
Solution :
Force exerted by one particle on another
Acceleration of heavier particle
Example 2:
Two stationary particles of masses M1 and M2 are at a distance 'd' apart. A third particle lying on the line joining the particles, experiences no resultant gravitational forces. What is the distance of this particle from M1 .
The force on m towards M1 is
The force on m towards M2 is
According to question net force on m is zero i.e. F1 = F2
Example :
Two particles of equal mass (m) each move in a circle of radius (r) under the action of their mutual gravitational attraction. Find the speed of each particle?
Solution :
For motion of particle