# Gravitation – Physics 7

## Gravitation – Physics 7

1.The distance of two planets from the sun are10¹³and 10¹² metres respectively. The ratio of time periods of these two planets is

(a)1/√10

(b)100

(c)10√10

(d)√10

2.The largest and the shortest distance of the earth from the sun are r1and r2. Its distance from the sun when it is at perpendicular to the major axis of the orbit drawn from the sun is

(a)r1+r2/4

(b)r1+r2/r1-r2

(c)2r1r2/r1+r2

(d)r1+r2/3

3.If the gravitational force between two objects were proportional to 1/R(and not as 1/R²) whereR is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

(a)1/R²

(b)R°

(c)R¹

(d)1/R

4.For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be

(a)11 km/s

(b)11√3km/s

(c)11/√3km/s

(d)33 km/s

5.A planet is moving in an elliptical orbit around the sun. If T, V,E and L stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct?

(a)T is conserved

(b)Vis always positive

(c)Eis always negative

(d)L is conserved but direction of vector L changes continuously

6.A satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?

(a)(3/4) mv²

(b)(1/2) mv²

(c)mv²

(d)– (1/2)m v²

7.A seconds pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

(a)comes down with uniform acceleration

(b)moves round the earth in a geostationary orbit

(c)moves up with a uniform velocity

(d)moves up with uniform acceleration

8.The mean radius of earth is R, its angular speed on its own axis is andthe acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite?

(a)(R²g/ω²)¾

(b)(Rg/ω²)¾

(c)(R²ω²/g)¾

(d)(R²g/ω)¾

9.A satellite A of mass m is at a distance of r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth’s centre. Their time periods are in the ratio of

(a)1 : 2

(b)1: 16

(c)1 : 32

(d)1 : 2√2

10.The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an anglee 45° to the vertical, then the escape velocityis[1993]
(a)11.2 × 2 km/s

(b)11.2 km/s

(c)11.2 /√2km/s

(d)11.2√2km/s

11.The distance of Neptune and Saturn from the sun is nearly 10¹³ and 10¹² meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

(a)10

(b)100

(c)10√10

(d)1000

12.A satellite in force free space sweeps stationary interplanetary dust at a rate dM/dt = αv whereM is the mass and v is the velocity of the satellite and α is a constant. What is the deceleration of the satellite?

(a)-αv²

(b)-αv²/2M

(c)-αv²/M

(d)-2αv²/M

13.The escape velocity from the surface of the earth is ve .The escape velocity from the surface of a planet whose mass and radius are three times those of the earth, will be[1995]
(a)ve

(b)3ve

(c)9ve

(d)1/3ve

14.What will be the formula of the mass in terms of g, Rand G (R= radius of earth)

(a)g²R/G

(b)GR²/g

(c)G/R/g

(d)gR²/G

15.A ball is dropped from a satellite revolving around the earth at a height of 120 km. The ball will

(a)continue to move with same speed along a straight line tangentially to the satellite at that time

(b)continue to move with the same speed along the original orbit of satellite

(c)fall down to earth gradually

(d)go far away in space

16.The period of revolution of planet A around theSun is 8 times that of B. The distance of A from the Sun is how many times greater than that of B from theSun?

(a)2

(b)3

(c)4

(d)5

17.The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

(a)44.8 km/s

(b)22.4 km/s

(c)11.2 km/s (remains unchanged)

(d)5.6 km/s

18.The escape velocity of a sphere of mass m is given by (G= Universal gravitational constant; M= Mass of the earth and Re= Radius of the earth)

(a)√GM/Re

(b)√2GMRe

(c)2GMm/Re

(d)√2GM/Re/Re

19.The escape velocity on the surface of earth is11.2 km/s. What would be the escape velocity on the surface of another planet of the same mass but 1/4 times the radius of the earth?

(a)22.4 km/s

(b)44.8 km/s

(c)5.6 km/s

(d)11.2 km/s

20.A body weighs 72 Non the surface of the earth.What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

(a)32 N

(b)28 N

(c)16 N

(d)72 N

21.Assuming earth to be a sphere of uniform density,what is the value of ‘g’ in a mine 100 km below the earth’s surface? (Given,R = 6400 km)

(a)9.65 m/s²

(b)7.65 m/s²

(c)5.06 m/s²

(d)3.10 m/s²

22.The potential energy of a satellite, having mass m and rotating at a height of 6.4 × 106m from the earth surface, is

(a)–mgRe

(b)– 0.67mgRe

(c)– 0.5mgRe

(d)– 0.33mgRe

23.With what velocity should a particlebe projectedso that its height becomes equal to radius ofearth?

(a)(GM/R)½

(b)(8GM/R)½

(c)(2GM/R)½

(d)(4GM/R)½

24.Assuming the radius of the earth as R, thechange in gravitational potential energy of abody of mass m, when it is taken from the earth’ssurface to a height 3Rabove its surface, is

(a)3 mg R

(b)3/4mgR

(c)1 mg R

(d)3/2mgR

25.The accelerationdue to gravity on the planet Ais 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surfaceof A. What is the height of jump by the sameperson on the planet B?

(a)23/m

(b)2/9m

(c)18 m

(d)6 m

26.Two spheres of masses m and M are situated inair and the gravitational force between them is F.The space around the masses is now filled witha liquid of specificgravity 3. The gravitationalforce will now be

(a)F/9

(b)3F

(c)F

(d)F/3

27.The density of a newly discovered planet istwice that of earth. The acceleration due togravity at the surface of the planet is equal tothat at the surface of the earth.If the radius ofthe earth is R,the radius of the planet would be

(a)½ R

(b)2 R

(c)4 R

(d)1/4 R

28.Imaginea new planet having the same densityas that of earth but it is 3 times bigger thanthe earth in size. If the accelerationdue togravity on the surface of earth is g’ and thaton the surface of the new planet is g’, then

(a)g’= g/9

(b)g’= 27g

(c)g’=9g

(d)g’=3g

29.For asatellitemoving in an orbit around theearth, the ratio of kinetic energy to potentialenergy is

(a)1/2

(b)1/√2

(c)2

(d)√2

30.The Earth is assumed tobe a sphere of radius R.A platform is arranged at a height R from thesurface of the Earth. The escape velocity of abody from this platform is f v, where vis itsescape velocity from the surface of the Earth.The value of fis

(a)1/√2

(b)1/3

(c)1/2

(d)√2

31.Two satellitesof earth, S1and S2are moving inthe same orbit. The mass of S1is four times themass of S2. Which one of the followingstatements is true?

(a)The potential energies of earth satellites inthe two cases are equal.

(b)S1and S2are moving withthe same speed.

(c)The kinetic energiesof the two satellitesare equal.

(d)The time period of S1is four times that ofS2.

32.Aroller coasteris designed such that ridersexperience“weightlesness” as theygo round thetop of a hill whose radiusof curvature is 20 m.The speed of the car at the top of the hill isbetween:

(a)14 m/s and 15 m/s

(b)15 m/s and 16 m/s

(c)16 m/s and 17 m/s

(d)13 m/s and 14 m/s

33.The figure shows elliptical orbit of a planet mabout the sun S. The shaded area SCD is twicethe shaded area SAB.If t1is the time for theplanet to move from C to D and t2is the time tomove from A to B then :

(a)t1= 4t2

(b)t1= 2t2

(c)t1= t2

(d)t1> t2

34.The radii of circular orbits of two satellitesA andB of the earth, are 4R and R, respectively. If thespeed of satellite Ais 3 V, then the speed ofsatellite B will be:

(a) 3 V/4

(b)6 V

(c)12 V

(d)3 V/2

35.Aparticle of mass Mis situatedat the centre ofa spherical shell of same mass and radius a. Thegravitational potential at a point situated at 2adistance from the centre, will be:

(a)-3GM/a

(b)-2GM/a

(c)-GM/a

(d)-4GM/a

36.Aplanet moving along an elliptical orbit is closestto the sunat a distance r1and farthest awayat adistance of r2. If v1and v2are the linear velocitiesat these points respectively, then the ratio v1/v2 is

(a)(r1/r2)2

(b)r2/r1

(c)(r2/r1)2

(d)r1/r2

37.A particle of mass m is thrown upwards from thesurfaceof the earth, with a velocity u. The massand the radius of the earth are, respectively, Mand R.G is gravitational constant and g isacceleration due to gravity on the surface of theearth. The minimum value of u so that the particledoes not return back to earth, is

(a)√2GM/R

(b)√2GM/R

(c)√2gR²

(d)√2GM/R²

38.Aparticle of mass M is situatedat the centre ofspherical shell of massM and radius a. Themagnitude of the gravitational potential at apoint situated at a/2 distance from the centre,will be

(a)2GM/a

(b)3GM/a

(c)4GM/a

(d)GM/a

39.The height at which the weight of a bodybecomes 1/16th, its weight on the surface of earth(radius R), is:

(a)5R

(b)15R

(c)3R

(d)4R

40.Aspherical planet has a mass MPand diameterDP. A particle of mass mfalling freely near thesurface of this planet will experience anacceleration due to gravity, equal to :

(a)4GMp/D²p

(b)GMpm/D²p

(c)GMp/D²p

(d)4GMpm/D²p

41.Ageostationary satellite is orbiting the earth ata height of 5Rabove that surfaceof the earth, Rbeing the radius ofthe earth. The time period ofanother satellite in hoursat a height of 2Rfromthe surface of the earth is :

(a)5

(b)10

(c)6√2

(d)6/√2

42.If veis escape velocity and v0 is orbital velocityof a satellitefor orbit close to the earth’s surface,then theseare related by :

(a)v0=√2v2

(b)v0= ve

(c)ve=√2v0

(d)v2=√2v0

43.Which one ofthe following plotsrepresents thevariationof gravitational field on a particle withdistance r due to a thin spherical shell of radiusR? (r is measured fromthe centre of the sphericalshell)

(a)FORr

(b)ROFr

(c)FORr

(d)FORr

44.Abody of mass ‘m’ is taken from the earth’ssurface to the height equal to twice the radius(R) of the earth. The change in potential energyof body will be[NEET 2013]
(a)2/3mgR

(b)3mgR

(c)1/3mgR

(d)mg2R

45.Infinite number of bodies, each of mass 2 kg aresituated on x-axisat distances 1m, 2m, 4m, 8m,….. respectively, from the origin. The resultinggravitational potential due to this system at theorigin will be

(a)-8/3 G

(b)-4/3 G

(c)–4 G

(d)– G

46.The radius of a planet is twicethe radius of earth.Both havealmost equal average mass-densities.If VP and VE are escape velocities of the planetand the earth, respectively, then

(a)VE = 1.5VP

(b)VP = 1.5VE

(c)VP = 2VE

(d)VE = 3VP

47.A particle of mass ‘m’ is kept at rest at a height3R from the surface of earth, where‘R’ is radiusof earth and ‘M’ is mass of earth.The minimumspeed withwhich itshould beprojected, sothatit does not return back, is (g is accelerationdueto gravity on the surfaceof earth)

(a)(GM/R)½

(b)(GM/2R)½

(c)(gR/4)½

(d)(2g/4)½

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