Physics Gravitation JEE question Paper for Practice with Answer 1

Physics Gravitation MCQ

1. GRAVITATION
GRAVITATION

2. GRAVITATION

3. GRAVITATION
1.Thegravitationalforcebetweentwobodiesisdecreasedby
36%.Whenthedistancebetweenthemisincreasedby3m.
Theinitialdistancebetweenthemis….
1) 6 m 2) 9 m 3) 12 m 4) 15 m
LEVEL-II
CLASS WORK
NEWTON’S LAWS OF MOTION
Solution:F
1
F
2
=
R
�
�
R
�
�
⟹
�
�
���
�
���
=
�+�
�
�
100
64
=
d+3
d
2
⟹
10
8
=
d+3
d
⟹d=12m

4. GRAVITATION
2.Masses2kgand8kgare18cmapart.Thepointwherethe
gravitationalfieldduetothemiszerois…
1) 6cm from 8kg mass
2) 6cm from 2kg mass
3) 1.8cm from 8kg mass
4) 9cm from each mass
Solution:
X =
d
m
2
m
1
+1
=
18
8
2
+1
=
��
�
=���

5. GRAVITATION
3.Twoleadballsofmassesmand5mhavingradiiRand2Rare
separatedby12R.Iftheyattracteachotherbygravitationalforce,
thedistancecoveredbysmallspherebeforetoucheachotheris…
1) 10 R2) 7.5 R3) 9 R4) 2.5 R
Solution:
R
2R9R
�����������������������������=�??????
�
��
�=�
��
�
�
��
�=��(�??????−�
�)
�
�=�.�??????

6. GRAVITATION
4.Threeequalmassesmareplacedatthethreeverticesofanequilateral
triangleofsidea.Thegravitationalforceexertedbythissystemon
anotherparticleofmassmplacedatthemidpointofaside……
1)
4Gm
2
3a2
2)
3Gm
2
4a2
3)
Gm
2
a2
4)
3Gm
2
a2
Solution:
�
�=−�
��
�+�
�=0
F
3
=
Gmm
3a2
4
�=
4Gm
2
3a2
�
��
�
m m m
m
�
�
3a
2
4
�
�/�

7. GRAVITATION
5.Twoparticlesofmassesmand2mareinitiallyatrestatinfinitedistance
apart.Theyareallowedtomovetowardseachotherduetomutual
gravitationalforce.Therelativevelocityofapproachofmwithrespect
to2mataseparatingdistanceof‘r’betweenthemis……
1)
���
�
2)
���
��
3)
���
�
4)
���
�
Solution:
V
rel
��
�
�
�+�
�= V
rel
��
�
�+��=
���
�

8. GRAVITATION
6.Imagineasatelliterevolvingaroundaverymassiveplanetinacircular
orbitofradiusRwithperiodT.Ifthegravitationalforceofattraction
betweenthesatelliteandplanetisinverselyproportionalto??????
�/�
.Then
??????
�
isproportionalto…..
1) R
3
2) ??????
�
�
Solution:
T
2
∝R
n+1
T
2
∝R
�
�
+�
∝R
�
�
3) ??????
�
�4) ??????
�
�

9. GRAVITATION
7.Thevalueofaccelerationduetogravityonthesurfaceofearthis‘X’.
Ataltitudeof‘h’fromthesurfaceoftheearth,itsvalueis‘Y’.If‘R’is
theradiusofearth,thenthevalueof‘h’is……
2)
Y
X
−1R
3)
Y
X
.R
4)
X
Y
.R
ACCELERATION DUETOGRAVITY&VARIATIONOFg
Solution:
�
�=
�
�+
�
??????
�⇒ y =
�
�+
�
??????
�
�+
�
??????
�
=
�
�
1+
�
??????
=
�
�
⇒
�
??????
=
�
�
-1h =
�
�
−�R
1)
�
�
−�R

10. GRAVITATION
8.Abodyreleasedfromcertainheightreachesthesurfaceoftheearth
aftertseconds.Ifthesamebodyisreleasedfromthesameheighton
themoon,itreachesthesurfaceafter(�
����=�/�)……
1) t/��
2) t/�s
3)�t s
4) ���
Solution:h =
�
�
g�
�
�
�
�
�
=
�
�
�
�
×
�
�
�
�
�
�
1 =
�
�
�
×
�
�
�
�
�
t
2
m6t
2
t
m= �t

11. GRAVITATION
9.IfRistheradiusoftheearth,theheightfromitssurfaceatwhichthe
accelerationduetogravityis9%ofitsvalueatthesurfaceis…..
1)
10R
2
2)
7R
3
3)
91R
9
4) 9 R
Solution:
�
�
�
�
=
??????+�
�
??????
�
���
�
=
??????+�
??????
�
⇒
??????+�
�
=
��
�
3??????+��=��??????⇒�=
�??????
�

12. GRAVITATION
10.RadiusoftheearthisR.Thedepthatwhichtheweightofabodyis
n%lessthanitsweightonthesurfaceoftheearthis……
�)�
�
??????
�
/���
2) nR/���
3) (���−�)/���
4) 100/100-n
Solution:g
d=��−
�
??????
���−�=����−
�
??????
�−
�
���
= 1 -
�
??????
�=�??????/���

13. GRAVITATION
11.Atunnelisdugalongadiameteroftheearth.Theforceonaparticle
ofmass‘m’placedinthetunnelatadistancexfromthecentreis….
�)
��
��
??????
�
??????
2)
GMem
R2
x
3)
GMem
R3x
4)
GMemR
3
x
�
�=��
�= ��(
R−d
R
) where
R-d = x , g =
GM
R2
(
R−d
R
) =
��
�
�
??????
�??????
Solution:
.
.
}
}
}
d
x
R -d

14. GRAVITATION
12.Assumingearthtobesphereofradius6400kmandgatitspoles10
ms
-2
,theminimumangularvelocityofrotationofearthforthe
weightofabodytobecomeszeroattheequatorwillbe……
�)
�
��
����
−�
2)
�
���
����
−�
3)
�
���
����
−�
4)
�
����
����
−�
Solution:
�
∅=�−????????????
�
���
�
∅
�
�=�−????????????
�
��
∅=�(�−????????????
�
)
��
∅=�⇒�=????????????
�
??????
�
=
�
??????
=
��
�����
??????=
�
���
rad/sec

15. GRAVITATION
13.Theaccelerationduetogravityattheequatorisgandangular
velocityofrotationofearthis??????
�.Theangularvelocityofrotationof
earthatwhichthevalueofaccelerationduetogravityattheequator
becomesg/2is……
�)??????
�
�
+
g
R
2) ??????
�
�
+
g
2R
3) ??????
�
�
−
g
R
4) ??????
�
�
−
g
2R
Solution:
�
�= �
�-R??????
�
�
�
�= �
�-R??????
�
�
�= g, �
�=
�
�
�
�-�
�=
�
�
= R(??????
�
-??????
�
�
)

16. GRAVITATION
14.Theweightsoftwoobjectsonelyingattheequatorandtheotherat
latitude��
�
onearthare100Neach.Iftheangularvelocityof
rotationofearthincreasessuchthattheobjectattheequator
becomesweightless(zeroN),theweightoftheobjectatlatitude��
�
willbe
�)100N
2) 50N
3) 25N
4) 0N
Solution:
�
∅=�−????????????
�
���
�
∅,

17. GRAVITATION
15.Iftheearthshrinkstohalfofitsradius,itsmassremainingsame,
thenweightofanobjectonthesurfaceofearthincreasesby
�)���%
2) 200%
3) ���%
4) ���%
Solution:
��=
���
??????
�

18. GRAVITATION
16.Ifdisthedistancebetweenthecentresoftheearthofmass�
�and
moonofmass�
�,thenthevelocitywithwhichabodyshouldbe
projectedfromthemidpointofthelinejoiningtheearthandthe
moon,sothatitjustescapesis…..
�)
�(�
�+�
�)
d
2)
�(��+��)
�d
3)
��(�
�+�
�)
d
4)
��(�
�+�
�)
d
ORBITAL&ESCAPEVELOCITIES

19. GRAVITATION
Solution:
−G��m
( d
2
)
-
−G��m
( d
2
)
+
1
2
�v
2
e= 0
??????������������������
=�����������������������������
KEY: 4

20. GRAVITATION
17.Particlesofmasses�
�and�
�areatafixeddistanceapart.Ifthe
gravitationalfieldstrengthat�
�and�
�are??????
�and??????
�respectively.
Then….
�)�
�??????
�+�
�??????
�=�
2) �
�??????
�+�
�??????
�=�
3) �
�??????
�−�
�??????
�=�
4) �
�??????
�−�
�??????
�=�
Solution: �
�+ �
�= �
??????
��
�+ ??????
��
�= �
??????
��
�+??????
��
�= 0

21. GRAVITATION
18.Theheightoftheorbitofageostationarysatelliteis5.635R(R=
radiusofearth).Ifthesatelliteisstoppedmomentarilyandthen
released,itmovestowardstheearth.Ignoringthefractionof
atmosphere,thevelocityofsurfaceofearthis(g-acceleratingdueto
gravityatthesurfaceofearth)(nearly)…..
�)
45g??????
4
2)
45g??????
53
3)
90g??????
53
4)
53g??????
45
Solution:(??????.�+�.�)
�������=(??????.�+�.�)
��������
-
GMm
6.625R
+0 = -
GMm
R
+
�
�
m�
�

22. GRAVITATION
19.TwosphericalmassivebodiesofmassesMand3Mareseparatedby
adistance4R.Theescapevelocityofaparticlefromapointatthe
centreofmassofthebodiesis….
�)
2GM
R
2)
GM
R
3)
10GM
3R
4)
20GM
3R
�
�=
m
2
d
m
1
+m
2
=
3M4R
4M
= 3R
Solution:
�
�=R
-
G�
�m
�
�
-
G�
�m
�
�
+
�
�
m�
�
�
= 0
(??????.�)
�=(??????.�)
�

23. GRAVITATION
20)Theescapevelocityofabodyfromtheearthisu.Whatistheescape
velocityfromaplanetwhosemassandradiusaretwicethatofthe
earth
�)��2) u 3) 4u 4) 16 u
Solution:
??????
�=
���
??????
??????
??????
??????
�
=
�
??????
�
�
×
??????
�
??????
??????
??????
??????
??????
�
=
��
�
�
�
×
??????
�
�??????
�
??????
??????=u

24. GRAVITATION
21.Threeparticlesofmasses1kg,2kgand3kgarearrangedatthe
verticesofanequilateraltriangleofsidelength1m.Thegravitational
potentialenergyofthesystemis(injoule)….
�)10 G 2) -10 G
3) -11 G 4)-36 G
Solution:
??????.??????.??????.=-
GM
1
M
2
r
12
+
GM
2
M
3
r
23
+
GM
3
M
1
r
31

25. GRAVITATION
22.Thespeedofasatellitethatrevolvesaroundearthataheight3R
fromearth’ssurfaceis(g=10m/�
�
atthesurfaceoftheearth,radius
oftheearthR=6400km.)….
�)��km�
−�2) 4km�
−�
3) 4�km�
−�4) 8km�
−�
Solution:
�
�=
��
(??????+�)
=
�??????
�
(??????+�)

26. GRAVITATION
23.ThekineticenergygiventoabodyisKsothatitmovesfromthe
surfaceoftheearthtoinfinity.Ifonly20%ofthiskineticenergyis
giventothesamebodyonthesurfaceoftheearth,itraisestoa
heightnRwhereRistheradiusoftheearth,thenn=……
�)�/3 2) 1/2
3) 3/4 4) none
Solution:
1
2
��
�
=
−G�m
??????+�
+
G�m
??????
1
2
��
�
�=
−G�m
??????

27. GRAVITATION
24.Threeidenticalparticleseachofmass“m’’arearrangedatthe
cornersofanequilibrium,thespeedwithwhichtheymustrevolve
undertheinfluenceofananother’sgravityinacircularorbit
circumscribingthetriangleis…..
�)
3Gm
L
2)
Gm
L
3)
Gm
3L
4)
3Gm
�
�
Solution:r =
�
�
�??????
�
�
=
��
�
�
�
�
m
m
m
o

28. GRAVITATION
25.Asolidsphereofuniformdensityandradius‘R’appliesa
gravitationalforceofattractionequalto�
�onaparticleplacedata
distance2Rfromthecentreofthesphere.Asphericalcavityof
radius‘
??????
�
’isnowmadeinthesphereasshowninthefigure.The
spherewithcavitynowappliesagravitationalforce�
�onthesame
particle.Theratio
�
�
�
�
is
�)�/�2) �/�
3) �/�
4) �/�
Solution:
�
�=
��
��
�
�??????
�
,�
�=
��(�/�)
�
�??????
�
/�
;�
�=�
�−�
�
R/2
R
2R
A

29. GRAVITATION
Thank you…