GRAVITATION

The Universal Law

Universal law of Gravitation

- Newton’s Law of gravitation states that every object in the universe attracts every other object by a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

- $F\propto M\times m$

- $F\propto \frac{1}{d^2}$



- $F=G\frac{Mm}{r^2}$, where G is the universal gravitation constant



- Value of $G=6.673\times {10}^{-11}N{m}^{2}k{g}^{-2}$


Acceleration due to gravity

F = mg and also $F=G\frac{Mm}{R^2}$
$g=G\frac{M}{R^2}$


Plug the values of $G=6.673\times {10}^{-11}N{m}^{2}k{g}^{-2},$


M(mass of Earth) $=6\times {10}^{24}kg$ and $R=6\times {10}^{6}m$ , to get the value 
of g as $\approx 9.8m{s}^{-2}$


This is the acceleration due to gravity and the acceleration felt by 

any freely falling body towards Earth. 


Value of g keeps changing due to the variation of Earth’s radius.


The Moon's Falling


Moon's revolution around Earth
- Moon revolves around Earth due to centripetal force, which is the force of gravity of the Earth.
- If the force of attraction between Earth and moon ceases, then the moon will continue to travel in a straight line path tangential to its 
orbit around Earth.


Centripetal force


When a body undergoes circular motion, it experiences a force that acts towards the centre of the circle. This centre-seeking force is called as centripetal force.


Free Fall


Freefall & motion


-    When an object is under free fall, acceleration due to gravity is constant at $g=9.8m{s}^{-2}$
-    Value of g does not depend on mass i.e any object big or small experiences the same acceleration due to gravity under free fall. 
-    All 3 equations of motion are valid for freely falling objects as it is under uniform motion.
-    Sign convention $\to$ towards earth g is +ve / away from earth g is -ve.


Weight and Mass


Weight and mass


- Mass of an object is the measure of its inertia and is constant throughout the universe. 
- Weight of an object keeps changing as the value of g changes. Weight is nothing but a force of attraction of the Earth on an object 
=  mg.

- Weight of an object on the Moon  is $\frac{1}{6}$ times the weight on Earth


Thrust and Pressure


Thrust & Pressure


- Force acting on an object perpendicular to the surface is called thrust. Effect of thrust depends on the area of contact. 
- Pressure is thrust per unit area. SI unit is pascal (Pa)
- Force acting on a smaller area applies more pressure than the same force acting on a larger area.


Pressure in fluids


- The pressure exerted by a fluid in a container is transmitted undiminished in all directions on the walls of the container.


Archimedes' Principle


Why objects float or sink


- The upward force exerted by a fluid on an object is known as upthrust or buoyant force.
- Magnitude of buoyancy depends on density of the fluid.


- If density of an object is less than the fluid, it will float.

- If density of object > fluid, it will sink.


Archimedes' principle


- When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.


Relative Density


Relative density


- $Relativedensity=\frac{Densityofasubstance}{DensityofWater}$


The Story of Gravity


Introduction to Gravitation : Kepler's laws


-    Orbit of a planet is an ellipse with the sun as its foci.
-    Line joining the planets and the sun sweeps equal areas in equal intervals of time.
-    Cube of mean distance of a planet from the sun ∝ Square of orbital time period T. $r^3\propto T^2$.