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Dwain Willis
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1 Basic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional to the cube of thei aius ) Diectly popotional to the fouth powe of thei aius 4) Invesely popotional to the squae of thei aius.. in the false statement Gavitational foce acts along the line joining the two inteacting paticles. ) Gavitational foce is inepenent of meium. ) Gavitational foce foms an action- eaction pai. 4) Gavitational foce oes not obey the pinciple of supeposition.. Among the following fin the wong statement Law of gavitation is fame using Newton s thi law of motion. ) Law of gavitation cannot explain why gavity exists. ) Law of gavitation oes not explain the pesence of foce even when the paticles ae not in physical contact. 4) When the ange is long, gavitational foce becomes epulsive. 4. Law of gavitation is not applicable if A) Velocity of moving objects ae compaable to velocity of light. B) Gavitational fiel between objects whose masses ae geate than the mass of sun. A is tue, B is false ) A is false, B is tue ) Both A & B ae tue 4) Both A & B ae false

2 5. Statement A: Moification of space by a mass paticle is calle gavitational fiel Statement B: Law of gavitation is a consequence of Action at a istance concept. A is tue, B is false ) A is false, B is tue ) Both A & B ae tue 4) Both A & B ae false 6. The eath evolves oun the sun in an elliptical obit, its spee is Going on eceasing continuously ) Geatest when it is closest to the sun ) Geatest when it is fathest fom the sun 4) Constant at all the points on the obit 7. How o you ivie total mass M into two pats so that the gavitational foce between them at a given istance is maximum? M, 4 4 ) M M, ) M 4M, 5 5 M M 4), 8. An infinite numbe of paticles each of mass 1kg ae place on the positive x- axis at 1m, m, 4m, 8m. fom the oigin. The magnitue of the esultant gavitational foce on 1kg mass kept at the oigin is 0 ) G ) G 4 4) 4 G 9. Two metal sphees of same mateial an aius ae in contact with each othe. The gavitational foce of attaction between the sphees is given by (k in a constant). k 4 ) k/ ) k/4 4) k 10. Thee unifom sphees each having mass m an aius kept in such a way that each two touches the othe. The magnitue of the gavitational foce on any sphee, ue to the othe two is 4 ) 4 ) 4)

3 11. Two paticles each of mass m move in a cicle of aius une the action of thei mutual gavitational attaction. Then spee of each paticle is ) 4 1. Thee ae two boies of masses 100kg an 10,000 kg sepaate by a istance of ) 4) 1 mete. At what istance fom the smalle boy, will the intensity of the gavitational fiel be zeo? ( 1/9m () 1/10m () 1/11m (4) 10/11m 1. If the istance between two boies is incease by 5%, then the % change in the gavitational foce is Deceases by 6% ) Inceases by 6 % ) Inceases by 64% 4) Deceases by 64 % 14. The time peio of evolution of a planet A aoun the sun is 8 times that of anothe planet B. The istance of planet A fom the sun is how many times geate than that of the planet B fom the sun ) ) 4 4) A planet evolves oun the sun. Its velocity at the neaest point, istant 1 fom sun, is v 1. The velocity of the planet at the fathest point istant fom sun will be. ( v v () 1 1 v () 16. A tunnel is ug along a iamete of eath. The foce on a paticle of mass m istant x fom the cente in this tunnel will be em ( x () em x emx () (4) v 1 1 emx (4)

4 17. Imagine a light planet is evolving oun a vey massive sta in a cicula obit of aius with a time peio of evolution T. If the gavitational foce of attaction between the sta an planet is popotional to -n, then T is popotional to n+1 ) n+ ) n 1 4) n 18. If two planets have thei aii in the atio x:y an ensities in the atio m:n, then the acceleation ue to gavity on them ae in the atio ( nx / my () mx / ny () ny / mx (4) my / nx 19. If a planet of mass m is evolving aoun the sun in a cicula obit of aius with time peio T, then the mass of the sun is GT ) GT ) GT 4) GT 1. A satellite is launche into cicula obit of aius aoun the eath while a secon satellite is launche into an obit of aius 1.0. The pecentage change in the time peios of the two satellites is 0.7 ) 1.0 ) 1.5 4). In a ouble sta system, two stas of masses m 1 an m sepaate by a istance otate about thei cente of mass. Then thei common angula velocity woul be 1 ) ( + m) 1 ) 4) ( + m) 1. The magnitues of the gavitational fiel at istance an fom the cente of a unifom sphee of aius an mass M ae an espectively. Then: 1. if 1 < an <. if > an 1 > 1 1. if 1 < an < 4. if 1 < an <

5 4. A soli sphee of unifom ensity an aius exets attactive gavitational foce 1 on a paticle place at a istance fom the cente of the sphee. Now a spheical cavity of aius is mae as shown. The emaining pat of the sphee exets a foce on the same paticle. Then 1 : 9 ) 7: 9 ) 5: 9 4) 1: 9 5. Newton's law of gavitation is univesal because It is always attactive ) It acts on all heavenly boies an paticles ) It acts on all the masses at all the istances an is not affecte by the meium 4) None of these Key ) 4 ) 4 4) 5) 6) 7) 4 8) 4 9) 0) 1 1 4) 15) 16) 4 17) 8) 19) 0) 4 ) ) 5)

6 Hints 7. Let the mass M is ivie into x an (M -x ) As xm ( x) o K (Mx - x ) o max, 0 x M k( M x) 0 x x M M The two pats ae, G(1 G(1 G( G G G a SG P 1 1/ G 1m o K π ρ π ρ + + cos 60 ( ) The gavitational foce between the two paticles povies the necessay centipetal foce fo otation mv V ( ) 4 1. Let the intensity be zeo at a istance fom 100kg mass. Then, G 100 G 10, 000 x (1 x)

7 Taking oot 1 10 o x 1 m x 1 x T 15. Accoing to law of consevation of angula momentum v v v O v M xm 16. G x O 17. If M 4. π x π x 4 m O x But m π m T T T + m π n m T h g, g1 k. xm, g k. yn 19. g : g :: xm : yn 1 sm π m T M s GT 0. a But cp fo otation

8 a a m ω 1.. ω T a ΔT Δ T ΔT Δ (0.0) 100 T m 1 ω m m ω m1 ω m 1+ m ( 1+ m). : If, then () if 1 < an < 1 If, then () if > an 1 > Gavitational foce on mass m ue to whole sphee m m 1 4 ( ) Gavitational foce ue to the emove sphee, M G m 8 m m m m

GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1

GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1 Einstein Classes, Unit No. 0, 0, Vahman Ring Roa Plaza, Vikas Pui Extn., New Delhi -8 Ph. : 96905, 857, E-mail einsteinclasses00@gmail.com, PG GRAVITATION Einstein Classes, Unit No. 0, 0, Vahman Ring Roa