GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle foce 4) Wek nucle foce. BASIC ORCE RELATIVE STRENGTH RANGE Gvittionl foce Long Rnge, Infinite Wek nucle foce 3 Extemely Shot Rnge <<fm Electomgnetic foce 36 Long Rnge, Infinite Stong Nucle foce 38 Shot Rnge, fm. The gvittionl foce is esponsible fo the ttction between pticles of vious bodies hving sme mss. 3. The electomgnetic foce is esponsible fo holding the toms togethe tht mke up the molecules. 4. The stong nucle foce is esponsible fo holding the potons nd neutons in the nucleus. 5. The wek foce is esponsible fo type of dioctive decy known s bet decy. 6. If m nd m e the msses of two bodies which e septed by distnce, then the gvittionl foce of ttction is given by mm G mm In vecto fom, G 3 Whee G is clled univesl gvittionl constnt nd is equl to 6.67 Nm Kg -. 7. Univesl gvittionl constnt does not depend upon the medium between the pticles (o) ny othe fctos. It is constnt evey whee in the univese. 8. The unifom cceletion poduced in feely flling body due to the gvittionl foce of plnet is known s cceletion due to gvity (g) 9. Gvittionl foce exists even when the pticles hve no physicl contct. This is clled ction t distnce o foce t distnce.. To ovecome the difficulties in the gvittionl lw, field concept is intoduced. The spce ound body in which its influence is thee is clled gvittionl field.. Accoding to Newton, gvittionl field is the distotion (distubnce) of spce due to the pesence of mtte. Gvittionl field, just like photons, is consideed s enegy pckets clled gviton. The est mss enegy of gvittion is zeo nd it tvels with velocity of light. Gviton is mss less BOSON with spin units.. Gvittionl field stength on the sufce of the eth is equl to the cceletion due to gvity. Though both quntities e equl in mgnitude hving the sme diections, they should be teted s two septe physicl quntities.
SHORT ANSWER ANSWERS. Stte the diffeent types of bsic foces in ntue? Ans. The bsic foces in ntue cn be clssified into fou types depending upon thei ntue nd eltive stength. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle foce 4) Wek Nucle foce. Gvittionl oces: ) These e long nge ttctive foces. b) These e wek foces nd e ppecible only when the intecting objects e mssive. c) These e independent of pesence of othe bodies nd the medium between the bodies. d) These e consevtive foces. e) These fom ction ection pis. f) Gvittionl foce exists even when thee is no physicl contct between them. Electomgnetic oce: )These e long nge foces b) These hve intemedite stength between electic nd mgnetic foces. C) Accoding to quntum field theoy electomgnetic foce between two chges is communicted by exchnge of Photons. Stong Nucle oces: ) These e esponsible fo holding potons nd neutons in the nucleus. b) These e between poton poton, poton-neuton nd neuton neuton c) These e shot nge ttctive foces. d) If the distnce between the nucleons is less thno.4 fm, these become epulsive. e) These e communicted by exchnge of π -mesons. Wek Nucle oces: ) These e esponsible fo β-dey nd simil pocess involving fundmentl pticles. b) These ct between leptons nd hdons. C) These e shot nge foces communicted by wek bosons.. Among the following, pick out the bsic foces involved. ) oce of fiction b) oces between two neutons in side the nucleus c) β- decy d) Muscul stength e) Moon evolving ound the eth f) Sufce tension g) Tension on sting h) Tides Ans. ) oce of fiction --- Electomgnetic oce b) oces between two neutons in side the nucleus -- Nucle oces c) β-decy --- Nucle oces d) Muscul stength --- Electomgnetic oce e) Moon evolving ound the eth -- Gvittionl foce f) Sufce tension --- Electomgnetic oce g) Tension on sting --- Electomgnetic oce h) Tides -- Gvittionl foce
3. Discuss the ntue of gvity. Ans. Evey body in the univese ttcts evey othe body. This foce of ttction between the bodies hving cetin mss is clled gvittionl foce o gvity.. Gvittionl foce between ny two bodies depends upon the poduct of the msses nd the distnce between them.. Gvittionl foce does not depend on the ntue of ttcting bodies nd is lwys ttctive. 3. Gvittionl foce between pi of bodies is centl foce. (i.e., it cts long the line joining thei centes of msses) 4. Gvittionl foce is long nge foce. 5. Gvittionl foce is wekest of ll fou bsic foces. 6. Gvittionl foce is consevtive foce. (i.e. The wok done by the gvittionl foce does not depends upon the pth tvesed) VERY SHORT ANSWER ANSWERS. Which is the wekest foce of ll the bsic foces in ntue? Ans. Gvittionl oce is the wekest foce.. Which is the stongest foce of ll the bsic foces in ntue? Ans. Nucle foce is the stongest foce of ll the bsic foces in ntue. 3. Among the following, which of the foces e long nge? (i) oce between two nucleons, (ii) oce between two electic chges, (iii) oce between the eth nd the moon. Ans. The gvittionl foce between eth nd moon is long nge foce 4. Stte the units nd dimensions of univesl gvittionl constnt. Ans. Dimensionl fomul of univesl gvittionl constnt is M - L 3 T - nd its unit is Nm Kg -. 5. Stte the limittion of Newton s thid lw biefly. Ans. Newton s lws do not pply when ) Velocities of objects e compble with velocity of light nd b) Gvittionl fields e vey stong. 6. Define gvittionl field. Ans. The spce ound mss in which its gvittionl foce of ttction is felt is known s gvittionl field. 7. Define gvittionl field stength. Is it scl o vecto? Ans. Gvittionl field stength t point in gvittionl field is defined s the gvittionl foce pe unit mss plced t tht point nd it is vecto quntity.
EXERCISE. Clculte the tio of electomgnetic nd gvittionl foces between two electons. (Chge of the electon e.6-9 C, mss of the electon m 9. -3 kg, pemittivity of fee spce ε 9 9 N m, univesl C gvittionl constnt G 6.67 - N m ) kg Sol: Electic foce e g e 4 πε G( m) e e 4πε nd Gvittionl foce 9 9 9.6 4.7 3 6.67 9. 4 g. The gvittionl foce between two identicl objects t seption of m is.667 mgwt. ind the msses of the objects (G 6.67 - Nm /kg nd g m/s ) Sol: m m m; m;.667 mg wt.667-6 N 6.67-7 N m 7 6.67 m 6.67 m kg. () 3. Two objects of msses 4 kg nd 3 kg e plced long X nd Y xes t espectively t distnce of m fom the oigin. An object of mss kg is kept t oigin of the co-odinte system. Clculte the esultnt gvittionl foce of ttction on the object t the oigin. Sol. oce on kg mss t the oigin due to 4 kg mss is given by m 4 X G 4G (long positive X - xis.) () oce on kg mss t the oigin due to 3 kg mss is given by G 3 Y 3G diected long positive Y - xis. om the pllelogm lw of vectos, + + cosθ ( G) ( G) ( G)( G) 4 + 3 + 4 3 cos 9 Let the esultnt mkes n ngle α with X 3 tn α.75 4 ' α 36 5 xis 6 9 5 G + G G
4. Thee pticles of identicl msses m e kept t the vetices of n equiltel tingle of ech side length. ind the gvittionl foce of ttction on ny one of the pticles. Sol: The foce of ttction on the pticle C due to A is given by, m A long CA The foce of ttction on the pticle C due to B is given by, m B long CB Resultnt of these two foces cn be found by pllelogm lw of vectos. A + B + A B cos θ + + cos 6 + + 3 3 sin 6 B sin θ Tn α A + B cos θ α 3 + cos6 3 i.e., long the pependicul bisecto to the opposite side. 5. ou pticles of msses m, m, 3m nd 4m e plced t the cones of sque of side length. ind the gvittionl foce on pticle of mss m plced t the cente of the sque. Sol Let the msses m, m, 3m, nd 4m e plced t the vetices of sque ABCD espectively. At the cente O mss m is plced. oce due to the mss t m on the mss t the cente is given by given by G m m A long OA. oce due to the mss t 3m on the mss t the cente is given by G m 3m 6 C long OC
A nd C e oppositely diected. Thei esultnt foce is given by 4 AC C A long OC. Similly the foce due to the msses m nd 4m e G m m 4 B long OB nd G m 4m 8 D long OD 4 Thei esultnt foce, DB D B long OD. The esultnt of AC nd DB is of mgnitude AC DB + As these two foces e pependicul to ech othe. 4 AC Tn α ; α 45 i.e., DB pllel to AD. 6. ind the point t which the gvittionl foce cting on ny mss is zeo due to the eth nd the moon system. The mss of the eth is ppoximtely 8 times the mss of the moon nd the distnce between the eth nd the moon is 3, 85,km (Such point is clled neutl point). Sol: Let m nd m be the msses of the eth nd the moon septed by distnce d. Conside n object of mss m t point P which is t distnce x fom m. The foce due to the mss m on the mss m is m towds m X The foce due to the mss m on the mss m is m towds m d x If the esultnt foce on the mss m is to be zeo, must be equl to in mgnitude s the two foces e oppositely diected. m m X d x ( ) d x m, x m
d x m d x m d m d m ; ; ; + x m x x m x m x m m + d x whee x is fom m. m Now m mss of the moon M; m mss of the eth8 M nd d3,85, Km 3,85, 3,85, x 38,5 km fom the moon. 8M 9 + + M 7. Two pticles of equl msses go ound cicle of dius R unde the ction of thei mutul gvittionl ttction. ind the speed of ech pticle. Sol. The two pticles e to be dimeticlly opposite so tht the gvittionl foce long the dius supplies the necessy centipetl foce. Gvittionl foce between the two pticles Centipetl foce GMm mv R R GM V 4R Execise. Two spheicl blls ech of mss kg e plced cm pt. ind the gvittionl foce of ttction between them. Ans. m m kg nd cm m om Newton lw of gvittion, m 6.67 7 4 6.67 N. The mss of bll is fou times the mss of nothe bll. When these blls e septed by distnce of cm, the gvittionl foce between 7 them is 6.67 N. ind the msses of the two blls. Ans. Mss of fist bll m 4m Mss of second bll m m Distnce between them cm m 7 oce between them 6.67 N m om Newton lw of gvittion, 7 6.67 4m m 6.67 m 5kg m kg nd m 5kg
3. Thee spheicl blls of msses kg, kg nd 3kg e plced t the cones of n equiltel tingle of side m. ind the mgnitude of the gvittionl foce exeted by kg nd 3kg msses on kg mss. Ans. om the figue. The foce of ttction of the kg bll on kg bll is m G ( ) G, long AB oce of ttction of the 3kg bll on kg bll is m G 3 ( 3) 3 G, long AC And Hee θ 6 Now esultnt foce on kg is given by, G G G G Cos 4 + 9 + 3 6 9 www.skshieduction.com + + Cosθ 4. The foce between two objects deceses by 36%. When the distnce between them is incesed by 4m, find the oiginl distnce between them. Ans. om Newton lw of univesl gvittion, α + 4 + 4 64 8 6 m G o 5. Thee equl msses m e plced t the thee vetices of n equiltel tingle of side.ind the gvittionl foce exeted by this system on nothe pticle of mss m is plced ) t the mid-point of side nd b) t the centoid of the tingle. Ans. () The foce of ttction of the pticle t A on the pticle t D, is 4 A long DA 3 3 The foce of ttction of the pticle t B on the pticle t D, is B 4 long DB / C 4 long DC ( / ) Since B nd C e equl nd opposite they cncel ech othe. Hence the esultnt foce cting on pticle t mid point (D) of side is 4 GM R A 3 (b) The foces A, B nd C cting on pticle t the centoid D of tingle e equl i.e., A B C
The ngle between B & is θ. C By using pllelogm lw of vectos,the esultnt of & is + + cos θ + + cos B C B C + / long DA Since this esultnt is equl nd opposite to A, the net foce cting on pticle t D is N R A 6. ou identicl msses M e kept t the cones of sque of side. ind the gvittionl foce exeted on one of the mss by the othe msses. Ans. Let fou equl msses M ech e plced t the be vetices of sque ABCD of side s shown in figue. Let the foces cting on the mss t A by othe thee e B, C & D espectively. GM Now, B long AB GM D, long AD C GM long AC ( ), The esultnt & is B + + cos 9 BD B D B D D GM GM GM BD + B sin θ B Also, Tnα cosθ C D B D Net esultnt foce R BD + C R GM GM + GM + B α 45 This is in the diection of 7. ou identicl msses m e kept t the cones of sque of side. ind the gvittionl foce exeted on point mss m kept t the cente of the sque. Ans. Let fou identicl msses m ech e plced t the vetices of sque ABCD espectively. Let nothe mss m is plced t the cente O. oce on the mss t the cente O due to mss t A is C
m A long OA. oce on the mss t the cente due to the mss t C is m GM C / long OC. The foces A nd C e equl nd opposite nd hence thei esultnt foce A C. Similly the foces due the msses t the opposite cones B nd D e equl nd opposite nd thei esultnt foce is lso equl to zeo. Hence the net esultnt foce cting on mss m t cente is zeo. 8. Two spheicl blls of mss kg nd 4kg e septed by distnce of cm. ind the distnce fom kg t which the gvittionl foce on ny mss become zeo. Ans. m Kg ; m 4Kg ; d cm Conside n object of mss m t point P which is t distnce x fom kg The foce due to mss m on the m mss m is towds m x The foce due to mss m on the mss m is m towds d x m If esultnt foce on the mss m is to be zeo, m m x d x 4 x ( x) x 4cm 9. Thee unifom sphee ech of mss m nd dius R e kept in such wy tht ech touches the othe two. ind the mgnitude of the gvittionl foce on ny of the sphees due to the othe two. Ans. The system is simil to thee identicl point mss plced t thee cones of n equiltel tingle of side R. Gvittionl foce cting on sphee A due to B is B long AB 4R Similly gvittionl foce cting on sphee A due to C is C long AC 4R Resultnt foce cting on sphee A is + + cos θ R B C B C + + R R R 4 4 4 3 4 R
ASSESS YOURSEL. Mention the type of the bsic foces involved in the following situtions? (i) Eth evolving ound the sun. (ii) Electon evolving ound the nucleus (iii) Neuton chnging into poton emitting electon nd ntineutino (iv) The ttctive foces between two potons inside the nucleus (v) The epulsive foce between two potons out side the nucleus Ans. i) Gvittionl foce, ii) Electomgnetic foce iii) Wek nucle foce, iv) Stong nucle foce nd v) Electo mgnetic foce.. Ange, the bsic foces in the scending ode of thei stengths nd mention which of the foces,wek nucle nd gvittionl is weke? Ans. Gvittionl foce < wek nucle foce <electomgnetic foce < stong nucle foce. Gvittionl foce is weke thn wek nucle foce. 3. Why cn t two pesons of sy kg stnding m pt not expeience ny gvittionl ttction between them? Ans. Accoding to Newton s lw of gvittion the foce of ttction between the two pesons is -7,which is vey smll. Hence two pesons of sy kg stnding m pt not expeience ny gvittionl ttction. 4. Wht cuses the tides in the ocens? Ans. The gvittionl foce of ttction between the moon nd the eth cuses the tides. 5. If hevie bodies e ttcted moe stongly by the eth, why don t they fll fste thn the lighte bodies? Ans. Since the cceletion due to gvity (g) is sme fo both hevie nd lighte bodies, both fll with the sme te.