GRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6

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1 GVITTION 1. Two satllits and o ound a plant P in cicula obits havin adii 4 and spctivly. If th spd of th satllit is V, th spd of th satllit will b 1 V 6 V 4V V. Th scap vlocity on th sufac of th ath is 11. km/s. What would b th scap vlocity on th sufac of anoth plant of th sam mass but 1/4 tims th adius of th ath? 44.8 km/s.4 km/s 5.6 km/s 11. km/s. If a body is to b pojctd vtically upwads fom ath s sufac to ach a hiht of 10 fom sufac of ath, (wh is th adius of ath), th vlocity quid to do so is If a spin balanc havin fquncy f is takn on moon (havin = / 6) it will hav a fquncy of 6f f / 6 6 f f 5. Two idntical sphs, ach with adius a placd so that thi cnts a at a distanc of 6. Th avitational foc of attaction btwn thm will b popotional to Th atio of potntial ny of an ath satllit to its total mchanical ny is 1 : : 1 4 : 1 1 : 1 6. Th foc of avitation is pulsiv consvativ ston non-consvativ Pa 1

2 8. If is th adius of ath, ω is its anula vlocity and p is th valu of acclation du to avity at th pols, thn ffctiv valu of acclation du to avity at th latitud λ = 60 0 will b qual to 1 ω 4 p ω 4 p p ω p 1 + ω 4 9. Th dpth d at which th valu of acclation du to avity bcoms n 1 tims th valu at th sufac, is ( = adius of th ath) n 1 n n n n n Two paticls of qual mass mov in a cicl of adius und th action of thi mutual avitational attaction. If th mass of ach paticl is M, th spd of ach paticl is 4 E 11. mass m is placd in th cavity insid a unifom hollow sph of mass M as shown in th fiu. What is th avitational foc on th mass m? m m ( ) m zo m 1. Two satllits and o aound a plant in cicula obits havin adii 4 and, spctivly. If th spd of satllit is v, thn spd of satllit is v 4v 6v 1 v Pa

3 1. plant is movin in an lliptical path aound th sun as shown in fiu. Spd of plant in positions P and Q a v 1 and v spctivly with SP = 1 and SQ = thn v 1 /v is qual to 1 1 P v 1 1 S v Q consonant Th hiht of th point vtically abov th ath s sufac at which th acclation du to avity bcoms 1% of its valu at th sufac is ( is th adius of th ath) Th distanc of th cnts of moon and ath is. Th mass of th ath is 81 tims th mass of th moon. t what distanc fom th cnt of th ath, th avitation foc will b zo? / / 4/ 9/ Th acclation du to avity on th sufac of th moon is 6 1 th of that on th sufac of ath and th diamt of th moon is on-fouth that of ath. Th atio of scap vlocitis on ath and moon will b Th valu of acclation du to avity at a hiht fom sufac of th ath is ( = adius of th ath and = acclation du to avity on ath sufac) zo Th piod of a satllit in a cicula obit aound a plant is indpndnt of th mass of th plant th adius of th obit th mass of th satllit all of th paamts ivn in options a, b and c Pa

4 19. Th tim piod of atificial satllit in a cicula obit of adius is T. Th adius of th obit in which tim piod is 8T is body is pojctd with scap vlocity 11. km/s fom ath s sufac. If th body is pojctd in a diction 0 0 anl to th vtical, its scap vlocity in this cas will b km/s 11. km/s 11. km/s non of ths 1. Th avitational foc of attaction btwn two sphical bodis, ach of mass 100 k, if th distanc btwn thi cnts is 100 m, is (G = Nm k ) N N 6.67 non of ths. Whn a satllit oin ound th ath in a cicula obit at a distanc fom a poton with kintic ny E. To scap to infinity, th ny which must b supplid to th lcton is E E 0.5 E E. plant volvs in lliptical obit aound th sun shown in th fiu. Th lina spd of th plant will b maximum at C S C 4. Th avitational foc btwn two point masss m 1 and m at spaation is ivn by m1m F = k. Th constant k 5. Th wiht of a body at th cnt of th ath will b zo M M infinity Pa 4

5 6. plant of mass M is volvin ound th sun in an lliptical obit. If its anula momntum is J thn th aa swpt p scond by th lin joinin plant to sun will b JM M J J M JM 7. Th avitational mass of a body on th ath is M. Th intial mass of th sam body on th moon will b zo 6 M M M/6 8. Two sphs of sam adius and sam matial a placd in contact with ach oth. Th avitational foc btwn thm is F 6 F 4 F F 1/ 9. n atificial satllit movin in a cicula obit aound th ath has a total ny E 0 (KE+PE). Its PE is E E 0 E 0 E 0 0. ostationay satllit obits aound th ath in a cicula obit of adius 6000 km. Thn piod of spy satllit obitin a fw hundd kilomts abov th ath s sufac ( ath =6400 km) will appoximatly b 1/ h h h 4 h 1. Two bodis of masss M 1 = m and M = 4m a placd at a distanc. Th avitational potntial at a point on th lin joinin thm wh th avitational fild is zo is zo 4Gm 6Gm 9Gm. Two sphs (idntical) of mass m and adius a spaatd by fom thi cnts. Th foc btwn thm is popotional to 4 4. Two sphs of masss m and M a situatd in ai and th avitational foc btwn thm is F. Th spac aound th masss is now filld with a liquid of spcific avity. Th avitational foc will now b F/9 F F F/ 4. t a hiht abov th sufac of th ath qual to th adius of th ath th acclation du to avity (acclation du to avity on th sufac of th ath = ) will b zo 4 Pa 5

6 5. Two idntical sphical masss a kpt at som distanc as shown. Potntial ny whn a mass m is takn fom sufac of on sph to th oth incass continuously m dcass continuously fist incass thn dcass fist dcass thn incass 6. body of mass m is doppd fom a hiht n abov th sufac of th ath (h is th adius of th ath). Th spd at which th body hits th sufac of th ath is ( n + 1) ( n 1) n ( n 1) n ( n + 1) 7. Two balls and a thown vtically upwads fom th sam location on th sufac of th ath with vlocitis and spctivly, wh is th adius of th ath and is th acclation du to avity on th sufac of th ath. Th atio of th maximum hiht attaind by to that attaind by is If th distanc btwn th ath and th sun w half its psnt valu, th numb of days in a ya would hav bn Two paticls of mass m and m a at th distanc apat. Und th mutual avitational foc thy stat movin towads ach oth. Th acclation of thi cnt of mass whn thy a at / is qual to Gm 4Gm 8Gm zo 40. Two paticl of masss 4 k and 8 k a spaatd by a distanc of 1 m. If thy a movin towads ach oth und th influnc of a mutual foc of attaction, thn th two paticls will mt ach oth at a distanc of 6 m fom 8 k mass m fom 8 k mass 4 m fom 8 k mass 8 m fom 8 k mass Pa 6

7 41. Two satllits and o aound th ath in cicula obits at hihts of and spctivly fom th sufac of th ath. ssumin ath to b a unifom sph of adius, th atio of th manituds of thi obital vlocitis is: satllit of mass m is obitin aound th ath at a hiht h abov th sufac of th ath. Mass of th ath is M and its adius is. Th anula momntum of th satllit is indpndnt of m M h non of ths 4. Two concntic shlls hav masss M and m and thi adii a and spctivly, wh >. What is th avitation potntial at thi common cnt? + + M m M m G G If a man at th quato would wiht (/5)th of his wiht, thn th anula spd of th ath would b satllit obitin aound ath of adius is shiftd to an obit of adius. How many tims th tim takn fo on volution incas? 8 tims tims.5 tims.8 tims 5 Pa 7

GRAVITATION 4) R. max. 2 ..(1) ...(2)

GRAVITATION 4) R. max. 2 ..(1) ...(2) GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body