2. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12

3. Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std:- 9 Sub:-Science Unit-Solid Waste: Ecofriendly Manegement

4. Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std:- 9 Sub:-Science Unit-Solid Waste: Ecofriendly Manegement

5. Rayat Shikshan Sanstha,Karmaveer Vidyaprabodhini,Madhya vibhag,Satara. Std:- 9 Sub:-Science Unit-Solid Waste: Ecofriendly Manegement

6. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12

7. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12

8. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 12.The pull of the earth. Centripetal force: – When a body performs uniform circular motion, the net force responsible for it is directed to wards the centre of the circle. It is called centripetal force. – Gravitational force: There exists a force of attraction between any two particles of matter in the universe such that the force depends only on the masses of the particles and the gravitational forces and the mutual attraction is called gravitation.

9. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Sir Isaac Newton(1642-1727) 1.English physicist and mathematician. 2. Discovered the binomial theorem, invented calculus. 3.Contribution in the fields of mechanics, gravitation, optic, heat and sound. 4.Newton’s laws of motion, Newton’s law of gravitation, explanation of motion of the moon, planet, comets, Newton’s law of cooling, Newton’s formula for speed of sound, Newton ‘s law of viscosity, corpuscular theory of light, work on dispersion of light, construction of a light, construction of a telescope using mirrors. 5. Exerted unique influence on science and scientific thought. 6.Books: Philosophiae naturals principia mathematica-The mathematical principles of natural philosophy (the most important and influential book on science), optics.

10. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Newton’s law of gravitation Every object in the universe attracts every other object with a force which is directed proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It acts along the line joining the centers. If two objects of masses m1 and m2 have their centers separated by a distance r, the gravitational force of attraction between the objects has magnitude F=G.m1m2 / r2, where G is the universal constant of gravitation. Earth’s gravity: The gravitational force exerted on a body by the earth’s gravity or simply the force of gravity. If r denoted the distance between the body and the center of the earth [r=R ( radius of the earth)], the gravitational force on the body due to the earth is F=G.mM / r2, where m is the masses of the body M is the mass of the earth If h is the altitude at which the body is located, r=R+h. F=G.mM / (R+h)2 and F =G.mM / R2 FOR h=0.

11. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Newton’s law of gravitation

12. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 12.2.1 importance of the universal law of gravitaion The universal law of gravitation successfully explanis : 1)The force that binds us to the earth. 2)The motion of moon around the earth. 3)The motion of the planets around the sun. 4)The tides of the sea due to the moon and the sun.

13. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 12.3force of gravition of the earth (earth’s gravity) Let us find the gravition force between two boys sitting very close to each other. Let the mass of one Boy be 40kg. And the other 50kg. Let the distance between them 0.5 m. consider to be point masses. we have, F = G m 1 m 2 r 2 Here r = 0.5m, m 1 = 40 kg m 2 = 50kg G= 6.67 x 10 -11 2 2 F = -11

14. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 = =533.6 x 10 N -11 -2 -9 -7

15. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Let us find the force betwwen a man of 60 kg and the earth Mass of earth = 6 X 10 24 kg F = G m 1 m 2 r 2 Here m 1 = 60 kg, m 2 = 6 X 10 24 kg and Radius of earth = r = 6.4 X 10 24 m F = 6.67 X 10 -11 X 60 X 6 X 10 24 ( 6.4 X 10 6 ) 2 = 586 N

16. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Solved example : 1)A Stone of mass 2 kg is falling form a certain height. Find the force of attraction between the earth and the stone. Also find its acceleration. Given : - Mass of earth (M) = 6 x 10 24 kg Mass of stone (m) = 2kg distance between stone and centre of the earth = radius of earth = 6.4 x x 10 6 kg

17. = 6.67 X 10 -11 X 60 X 6 X 10 24 ( 6.4 X 10 6 ) 2 ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Solution : F = G Mm R 2 = 6.67 X 10 -11 X 6 X 10 24 x 2 ( 6.4 X 10 6 ) 2 = 19.6 N Acceleration (g) = F m g = 19.6 2 = 9.8 m/s 2

18. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 2) If the force of gravitation between the earth and a body of mass ‘m’ is 9 x 10 7 N., then find the mass of the body. Mass of the earth = 6x 10 24 kg and radius of the earth = 6.4 x 10 6 m Given :- F = 9 x 10 7 N R = 6.4 x 10 6 m M = 6 x 10 24 kg G = 6.67 x 10 -11 Nm 2 / kg solution:- F = G Mm R 2 9 x 10 7 = 6.67 X 10 -11 X 6 X 10 24 x m ( 6.4 X 10 6 ) 2 M= 9 x10 7 x ( 6.4 X 10 6 ) 2 = ( 6.67 X 10 -11 X 6 X 10 24 ) = 9.2 x10 6 kg

19. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Acceleration due to gravity – The acceleration produce in a freely falling body due to the earth’s gravitational due to gravity(g). It is directed towards the earth’s centers. Is value is maximum at the poles and minimum at the equator. g decreases with altitude. g also decreases as we go from the earth’s surface towards the earth’s center. At the centers of the earth g become zero. Mass : The mass of a body is the quantity of matter contained in it. If does not have directed. It can never be zero and it does not change from place to place. It is a measure of the inertia of the kilometer (kg) and the CGS unit is the gram(g).

20. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Weight: The weight of a body is the gravitational forces with which the earth attracts it towards the earth’s centre. On the earth’s surface, weight, w= G. mM/ R2 =mg. Weight changes just like acceleration due to gravity. The SI unit of weight is the newton (N) and the CGS unit is the dyne. Free fall When the only force acting on a falling body is that due to the earth’s gravity. The motion of the body is called free fall. Assuming g to have the same magnitude everywhere near the earth’s surface, we have, the acceleration of the body, a=g. In the usual notation. V= u + at = u + gt, S = ut + 1/2gt and V =u + 2as = u + 2gs. The acceleration due to gravity is always downward. Hence, it is considered negative

21. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Solved Examples 1) calculate the value of the acceleration due to gravity g m on the surface of the moon.with the hellp of following data. M m = mass of moon = 7.4 x 10 22 kg R m = radius of moon =1724 km = 1740000m =1.74 x 10 22 G= 6.67 x 10 -11 Nm 2 /kg 2. Given = The acceleration due to gravity of the moon is given by equation. g m = G Mm R 2 = 6.67 X 10 -11 X 7.4 X 10 22 x m Gm = 1.63m/s 2 but the value of ge i.e g on earth is 9.8 m/s 2 Gm (1.74 x 10 6 ) 2 ge = 1.63 9.8 1616

22. Activity: Take small stone of various masses and tie them to a string one by one. Then hold the string and give rotational motion to it and release the string. Observe and note the motion of the string and the stone. What do you observe ? Ans.:- The stone and the string move along curve and fall to the ground. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12

23. Activity:- 1)Throw a ball in upward direction and observe its motion.What do you find? Ans.:- As the ball moves up its speed goes on decreasing. It becomes zero at highest point. The ball then falls with increasing speed. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12

24. ¸üµÖŸÖ ×¿ÖÖÖ ÃÖÓãÖÖ, ú´ÖÔ¾Ö߸ü ×¾ÖªÖ¯ÖϲÖÖê׬֭Öß, ´Ö¬µÖ ×¾Ö³Ö֐Ö, ÃÖÖŸÖÖ¸üÖ Std- 9 th sub- sci.&tech. Unit- 12 Activity:- The two balls of the different masses, go to the top of a building, drop them simultaneously and observe what happens to the balls. Ans.:- The balls reach the ground almost at the same time.