Tiêu đề 3. GRAVITATION WS-1 (88-98).pmd.pdf ✅

Olympiad Class Work Book VIII – Physics (Vol – III) CONCEPT FLOW CHART Born : 27 December 1571, Weil der Stadt, Germany Died : 15 November 1630, Regensburg, Germany Education : Eberhard Karls University of Tübingen (1591–1594), MORE Johannes Kepler was born on December 27, 1571, in the town of Weil der Stadt, which then lay in the Holy Roman Empire, and is now in Germany. Johannes Kepler is a pioneer in the field of Astromomy. He born in free imperial city of germany. He contributed in the field of Geometry and optics also. He founded the theory of celestial mechanics to explain planetary motion. The Epitome Astronomiae copernicanae was an astronomy book published by Kepler. JOHANNES KEPLER (27-12-1571 TO 15-11-1630) Gravitation Newton’s law of universal gravitation Johannes Kepler’s law Relation between g & G Variation of g with depth and height Gravitational field strength Gravitational potential energy Orbiting satellite . .
VIII – Physics (Vol – III) Olympiad Class Work Book GRAVITATION Introduction: Have you ever wondered whether we would still be studying about gravitation if a stone had fallen on newton’s head instead of an apple? anyway, the real question is why does an apple fall down rather than go upward? The motion of celestial bodies such as the moon, the earth, the planets etc., has been a subject of great interest for a long time. Famous Indian astronomer Aryabhatta studied these motions in great detail and wrote his conclusions in his book “Aryabhattiya” he proposed that the earth revolves about its own axis and moves in a circular orbit about the sun, and the moon moves in a circular orbit around the earth About a thousand years after Aryabhatta, the brilliant combination of Tycho Brahe 1546 1601   and Johannes Kepler 1571 1630   studied the planetary motion in great detail. The year 1665 was very fruitful for Isaac newton. In this year he focused his attention on the motion of the moon about the earth in 1687, Newton published an article “Philosophia naturalise principia mathematica” In this article newton explained planetary motion with his law of universal gravitation. Newton’s universal law of Gravitation: Every particle in this universe attracts other particle with a force which is di- rectly proportional to the product of their masses and inversely proportional to the square of the distance between them. m1 r m2 F12  F21  F12   Force on mass m1 due to mass m2 F21   Force on mass m2 due to mass m1  F m m  1 2 and 2 1 F r  1 2 2 m m F r  1 2 2 Gm m F r 
Olympiad Class Work Book VIII – Physics (Vol – III) Where “G” is known as universal constant of gravitation. Important points: 1. The value of G is -11 2 2 6.67×10 Nm /Kg 2. It’s dimensional formula is -1 3 -2   M L T .   3. G is a scalar quantity and it’s value is same throughout the universe. 4. Gravitational force is the weakest of all the forces but has the longest range. 5. Gravitational force does not depend on the medium that lies between the two bodies. 6. Gravitational force obey newton’s third law of motion. i.e., the gravitational force of attraction between two bodies form action and reaction pair. 6. Gravitational force is conservative and central force. 7. Gravitational force is one of the four fundamental forces of nature. 8. The force of attraction between any two masses by virtue of their mass is called gravitational force. Gravitational Field Intensity (E): Gravitational force per unit mass is called gravitational field intensity. F E = m   SI unit of gravitational field intensity is N/kg Dimensional formula of gravitational field intensity is 0 1 -2   M L T .   Gravitational field intensity due to point mass: r O M p m 1. The intensity of gravitational field at a distance ‘r’ from a point mass M is given by 2  GM E r 2. The direction of  E is in the direction of  F . 3. The value of E is zero at r   . 4. The variation of E with distance r is as shown.
VIII – Physics (Vol – III) Olympiad Class Work Book E r 2 Principle of superposition: Gravitational field intensity at a point can be found out by using the principle of superposition. According to principle of superposition the net Gravitational field intensity at a point is equal to the vector sum of all individual Gravitational field intensities acting at that point. Mathematically 1 2 3 E E E E net ............         or 1 2 3 F F F F net ............         Null point: It is the point in a gravitational field at which resultant field intensity is zero. Since gravitational force is always attractive, null point always forms between the two masses. m1 E1 E2 m2 r x Consider two particles of mass m and m 1 2 separated by certain distance r. Let x be the distance of null point from m .1 E E 0 1 2     E E 1 2     E E 1 2      1 2 2 2 m m G =G x r-x Simplifying the above equation, we get 2 1 r x= m 1+ m