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.

Newton's Law of Gravitation

$F\propto {m}_{1}{m}_{2}\, and\, F\propto \frac {1} {{r}^{2}}\, so\, F\propto \frac {{m}_{1}{m}_{2}} {{r}^{2}}$

$F=\frac {G{m}_{1}{m}_{2}} {{r}^{2}}\, \, where\, G\, is\, Universal\, Gravitational\, Constant$

Vector form of Newton's law of Gravitation :

let

${r}_{12}=displacement\, vector\, from\, {m}_{1}\, to\, {m}_{2}$

${r}_{21}=displacement\, vector\, from\, {m}_{2}\, to\, {m}_{1}$

${F}_{21}=Gravitational\, force\, exerted\, on\, {m}_{2}\, by\, {m}_{1}$

${F}_{12}=Gravitational\, force\, exerted\, on\, {m}_{1}\, by\, {m}_{2}$

${F}_{12}=-\frac {G{m}_{1}{m}_{2}} {{{r}_{21}}^{2}}{r}_{21}$

Negative sign shows that :

(i) The direction of ${F}_{12}$ is opposite to that ${r}_{21}$

(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

$F=\frac {G{m}_{1}{m}_{2}} {{r}^{2}}\, \, =\frac {6.67*{10}^{-11}*182} {{0.5}^{2}}=5.34*{10}^{-10}N$

Acceleration of heavier particle

$\frac {F} {{m}_{2}}=\frac {5.34*{10}^{-10}} {2}=2.67*{10}^{-10}{ms}^{-2}$

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

${F}_{1}=\frac {G{M}_{1}m} {{r}^{2}}$

The force on m towards M2 is

${F}_{2}=\frac {G{M}_{2}m} {{(d-r)}^{2}}$

According to question net force on m is zero i.e. F1 = F2

$"\frac$

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

$"\frac$

Post By : Preeti Rai 15 Mar, 2019 1531 views Physics

What is NEWTON'S LAW OF GRAVITATION - Concept with example.

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