Gravitation – Summary
Latest CBSE syllabus topics –
Gravitation – Gravitation, universal law of gravitation, force of gravitation of the earth (earth’s gravity), acceleration due to gravity, mass and weight, free fall.
Flotation – Thrust and Pressure, Archimedes’ Principle, Buoyancy, Elementary idea of relative density.
Latest Maharashtra SSC Board syllabus topics –
The Pull of the Earth – Gravitation, universal law of gravitation, force of gravitation of the earth (earth’s gravity), acceleration due to gravity, mass and weight, free fall.
Why Bodies Float – Floating Bodies: Thrust and Pressure, Archimedes’ Principle, Buoyancy, Idea of relative density.
- Centripetal force – The inward force on a body moving in a curved path around another body is called centripetal force.
- When we whirl around a stone attached to a string, the force keeping the stone towards the centre of the circle is centripetal force.
- Gravitational force – It is the force of attraction between any two masses in the universe.
- Force of gravitation due to earth is called gravity. The more remote the body, the less the gravity.
- The force of gravitation is a force of attraction only.
- Universal Law of Gravitation – “The force of attraction or gravitation between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them”;
F = GMm / d2
or G = Fd2 / Mm
G is known as universal gravitational constant and its SI unit is Nm2/ kg2.
- The value of G is 6.67 x 10-11 Nm2 / kg2 and in CGS system, it is 6.67 x 10-8 dyne-cm2/ gm2.
- Importance of the Universal Law of Gravitation – It explains several physical phenomena such as –
(a) the gravitational force of attraction binds us to the Earth.
(b) the moon revolves around the Earth.
(c) the planets revolve around the Earth.
(d) high tides and low tides of the oceans.
- All objects falling towards the Earth under the action of gravitational force of the Earth alone are said to be in “free fall”.
- Acceleration due to Gravity – The acceleration experienced by a body in free fall in a gravitational field is called acceleration due to gravity. It is represented by ‘g’.
g = GM / R2
- The value of g on the surface of the earth is 9.8 ms-2.
- Gravitation is a weak force unless large masses are involved.
- The force of gravity decreases with altitude. It also varies on the surface of the earth, decreasing from poles to equator.
- Mass – It is the amount of matter that a body contains, and a measure of the inertial property of that body, that is, of its resistance to change of motion (Inertia). The SI unit of mass is the kilogram (kg). Mass is different from weight. Inertial mass and gravitational mass are identical.
- Weight – It is the measure of the attraction of the earth for a given mass (Gravitation). The SI unit of weight is the newton (N).
W = m x g
The weight is a force acting vertically downwards; it has both magnitude and direction.
- Because of the relationship between weight and mass, these concepts are frequently confused (W a m). The mass of an object remains constant everywhere, that is on the earth or on any planet whereas its weight changes on different locations.
- If you were to leave the Earth and go to the Moon, your weight would change but your mass would remain constant.
Weight of the object on the moon Wm = (1/6) x Its weight on the earth We.
- Thrust – It is a force that is exerted on an object by the expulsion or acceleration of mass in a particular direction.
- Pressure – The thrust on unit area is called pressure.
Pressure = Thrust / area
The SI unit of pressure is pascal = 1 N/m2. Other units are bar and millibar.
1 bar = 105 pascals
1 millibar = 102 pascals
1 atmospheric pressure (atm) = 1.013 x 105 pascals or 1.013 bar.
- Large pressure is exerted on a smaller surface and smaller pressure is exerted on a larger surface by the same force.
- Fluid (liquid and gases) exert pressure on the base and wall of the container that hold them.
- Upthrust or Buoyant force – It is the force that a liquid or gas directs upwards on an object that is floating on it. It depends on the density of a liquid.
- Buoyancy – It is the ability of a liquid to make things float in it. The property of the liquid, due to which a liquid exerts upthrust is called buoyancy.
If the density of a body is less than the density of liquid, it will float, and if the density of a body is more than the density of liquid, the body will sink.
- Archimedes’ principle or Law of buoyancy -“any body partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.” The weight of an object acts downward, and the buoyant force provided by the displaced fluid acts upward. If these two forces are equal, the object floats.
- Relative density = density of a substance / density of water