Gravitation Questions and Answers

At what height the gravitational field reduces by 75 the gravitational field at the surface of earth a R b 2R c 3R d 4R where R is the radius of earth lid opbere

A d J 34 P r is magnitude of physical quantity as a function of r distance from centre of spherical distribution of radius R Match the following columns and select the correct option from the codes given below Column I A P r B P r n r R C P r D P r r R r R r R a A 4 b A 2 B 3 B 4 Column II 1 P r is variation of gravitational potential for a uniform volumetric r spherical distribution of mass 2 P r is variation of gravitational potential for a uniform spherical shell 3 P r is variation or gravitational field intensity for a uniform volumetric spherical distribution of mass 4 P r is variation of gravitational field intensity for a uniform spherical shell C 2 D 1 C 3 D 1 d 35 A roc surfac radius the m surfa a F C 36 Tw int to T d

Two satellites of earth S and S2 are moving in the same orbit The mass of S is four times the mass of S Which one of the following statements is true 519 1 The kinetic energies of the two satellites are equal 2 The time period of S is four times that of S 3 The potential energies of earth and satellite in the two cases are equal 4 S and S are moving with the same speed

Two bodies of masses mand Mare placed at distance d apart The gravitational potential V at the position where the gravitational field due to them is zero Vis G Ov m M G Ov 00 V Ov GM d

A comet travels around sun in elliptical orbit Its mass is 105 kg When it is 2 5 x 1010 m away its speed is 2 x 10 m s The change in kinetic energy when it has reached 5 10 m away from sun is velocity and position vector of comet is perpendicular to each other at both instant 3 2 x 107 J 2 4 10 J 2 5 x 1013 J 4 8 x 10 2 J

Que 9 A rocket is launched straight up from the surface of the earth When its height is one fourth of the radius of the earth its fuel finished The minimum velocity which the rocket must have when it s fuel finished and if it is to escape from the gravitational pull of the earth is escape velocity on surface of earth is 11 2 km s O1 km s 5 km s O 10 km s O 15 km s

Which of the following statements is true about acceleration due to gravity by Earth g increases in moving away from the centre if r R g decreases in moving away from the centre if r R g is zero at the centre of earth g decreases if earth stops rotating on its axis

The figure shows elliptical orbit of a planet m about the sun S The shaded area SCD is twice the shaded area SAB If t be the time for the planet to move from C to D and t2 is the time to move from A to B then m B A O t 1 S O t 8t t 4t t 2t C D

A rocket starts vertically upwards with speed vo Choose the correct option s R is the radius of the earth a Speed v at a height h is given by 2gh 1 h R b The maximum height reached by the rocket fired with a speed of 90 of escape velocity is 2 26 R c The maximum height reached by the rocket fired with a speed of 90 of escape velocity is 4 26 R d Speed v at a height h is given by 18 12 2gh h

d C and A are the kinetic and potential energies and B the total energy of the satellite 69 Two satellites of earth S and S are moving in the same orbit The mass of S is four times the mass of S Which one of the following statements is true a The potential energies of earth and satellite in the two cases are equal b S and S are moving with the same speed c The kinetic energies of the two satellites are equal d The time period of S is four times that S

1 The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M to transfer it from a circular orbit of radius R to another of radius R R R is a GmM 1 RR c 2GmM 1 d GmM 1 R R R b GmM 1 R

A geostationary satellite is at a height h above the surface of earth If earth radius is R 2 R a The minimum colatitude on earth upto which the satellite can be used to communicate is sin R R h b The maximum colatitude on earth upto which the satellite can be used to communicate is sin R R h c The area on earth escaped from this satellite is given as 2 R 1 sin 0 d The area on earth escaped from this satellite is given

Two bodies each of mass M are kept fixed with a separation 2L A particle of mass m is projected from the midpoint of the line joining their centres perpendicular to the line The gravitational constant is G The correct statement is a The minimum initial velocity of the mass m to escape

Two particles of equal mass m go round a circle of radius R under the action of their mutual gravitational attraction The speed of each particle is O ZAR 1 2R Gm OGm 2R O 1 Gm 2 R 4Gm R

here are three planets in circular orbits around a fixed star at distances a 4a and 9a espectively in same sense say anticlockise At time t 0 the star and the three planets are na straight line The period of revolution of the closest planet is T What minimum time fter t 0 will they again be in the same straight line A 8 T B 27 T C 108 T D 512 T

c 3 57 x 10 m d 3 57 x 10 m WEIGHTLESSNESS An astronaut experiences weightlessness in a space satellite It is because a the gravitational force is small at that location in space b the gravitational force is large at that location in space c the astronaut experiences no gravity d the gravitational force is infinitely large at that location in space

18 Two spheres each of mass M and radius R are separated by a distance of r The gravitationa potential at the midpoint of the line joining the centres of the spheres is GM a c GM 2r b d 2GM 4GM

height he can jump a Im b 0 8 m c 0 5 m d 1 25 m 36 If the mass of sun were ten times smaller and gravitational constant G were ten times larger in magnitudes then which one of the following statements is incorrect a Walking on ground would become more difficult b The acceleration due to gravity on earth will not change c Raindrops will fall much faster d Airplanes will have to travel much faster 42 2 e S

1 Acceleration due to gravity everywhere on the equator of a spherical asteroid of radius R is go A spherical cavity with its centre in the equatorial plane inside the asteroid is made and then acceleration due to gravity is measured everywhere on the equator The minimum accelerations due to gravity is observed smaller than go by n fraction of go at a point and at its diametrically opposite point acceleration due to gravity is observed smaller than go by 12 fraction of go Find radius of the cavity and depth of its centre

Q 85 At a certain angular velocity objects placed at equator loose contact with earth s surface Find the corresponding height of the geostationary satellite a 6400 kms b 3200 kms c 3600 kms

For technology project a student has built a vehicle of total mass 5 kg that moves itself As shown in the figure it runs on four light wheels A reel is attached to one of the axles and a cord originally wound on the reel goes up over the pulley attached to the vehicle to support an elevated load After the vehicle is released from rest the load descends very slowly unwinding the cord to turn the axle and make the vehicle move forward Friction is negligible in pulley and axle bearings The wheels do not slip on the floor The reel has been constructed with a conical shape so that load descends at a constant low speed while the vehicle moves horizontally across the floor with a constant acceleration reaching a final velocity of 3 m s Mark the CORRECT option s A Magnitude of impulse on the vehicle due to friction of floor is 15 N s B Work done by friction force between tyre and floor is 27 J C Change in gravitational potential energy of earth and cart system is 27 J D The acceleration of the cart is due to friction force from the ground

A particle is projected from a point A which is at a distance 8R from the centre of the earth and with speed V in a direction making 30 with the line joining the centre of the earth and point A as shown Find the speed V if the particle passes grazing the surface of the earth Consider gravitational interaction only between these two use GM 6 4 x 107 m s R 8R Fot 30 R 1000 112 m s 15 m s 8000 2 8000 2 m s None of these

A tunnel is dug along the diameter of the earth There is a particle of mass m at the centre of the tunnel Find the minimum velocity given to the particle so that it just reaches to the surface of the earth A B GM R GM 2R 2GM C R D it will reach with the help of negligibl

In order to shift a body of mass m from a circular orbit of radius 2R to a higher orbit of radius 4R around the earth Where R is radius and M is mass of earth the work done on the body is Answer Your Attempt GMm Correct answer Rate this questic

With what angular velocity the earth should spin in order that a body lying at 60 latitude may become weightless R Radius of earth g acceleration due to gravity on the surface of the earth All quantities are measured in S l unit 0 2 PARR 0 1

A small satellite of M and radius a revolves around a heavy planet M in a circular orbit such that it always faces the planet during its revolution The closest distance that the planet can get so that the dust particles from the satellite surface does not leave the surface is 1 3 xGM a where x is

Section I Straight Objective Type This section contains 5 multiple choice questions Each question has 4 choices a b c and d out of which ONLY ONE is correct 1 An asteriod of mass m is approaching carth initially at a distance of 10R with speed v It hits the earth with a speed v R and M are radius and mass of earth then 2Gm M R 10 b 1 1 2GM R 2GM R 4 1 10 d v 26m 1 11 Re 10

19 A particle of mass M is situated at the centre of a spherical shell of same mass and radius R The gravitational potential at a point situated at distance from the centre will be R 2 3GM a b R GM d c 2GM R 4GM R 55

The current in the primary circuit of a potentiometer is 0 2 A The specific resistance and cross section of the potentiometer wire are 4 x 107 ohm m and 8 x 10 7 m respectively The potential gradient will be equal to 0 2 V m 1 V m 0 5 V m 0 1 V m

8 Figure shows elliptical path abcd of a planet around the sun S such that the 1 area of triangle csa is the area of 4 the ellipse See figure With db as the major axis and ca as the minor axis If t is the time taken for planet to go over path abe and t2 for path taken over cda then 1 31 1 2 1 21 3 1 31 S C a b

A coil in the shape of equilateral triangle of side 0 02 m is suspended from the vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of 5x10 2 T When a current of 0 1 A passes through it and the magnetic field is parallel to its plane then couple acting on the coil is 1 8 65 x 10 7 N m 2 6 65 x 10 7 N m 3 3 35 x 10 7 N m 4 3 91 x 10 7 N m

A satellite is revolving around earth at a height 2R above earths surface If the satellite is stopped and then released then velocity of body on reaching to earth s surface g is acceleration due to gravity on surface and R is radius of earth 2gR 3 4gR 3 2gR 4gR Marks 4 1

20 An asteroid was located at a distance of 5R with respect to earth s centre and moving with a speed v at an angle of 37 with the line connecting them as shown re 37 1 5v 2 3v 3 2v R Earth If the asteroid just grazes the earth s surface find its maximum speed

Consider a system consisting of three masses on the x axis Mass m1 1 00 kg is at x 1 00 m mass m2 2 00 kg is at x 2 00 m and mass m3 3 00 kg is at x 3 00 m What is the total gravitational potential energy in J of this system O 6 34 10 10 O 5 6 10 10 300 0

A spherical shell is cut into two pieces along a chord as shown in the figure P is a point on the plane of the chord The magnitude of gravitational field at P due to the upper part is 1 and that due to the lower part is 12 What is the relation between them OD 11 12 1 12 1 12 No definite relation

A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius The centre of the ring is directly above the centre of the sphere at a distance r 3 as shown in the figure The gravitational force exerted by the sphere on the ring will be GMm a b 8p GMm 8 c 3 d GMm 4p GMm 8r 3 T 3r 2r

Two particles of mass m and 3m are initially at rest and infinite distance apart Both the particles start moving due to gravitational attraction At any instant their relative velocity of approach is separation at that instant Find n nGm d where d is their

8 Gravitational potential on the surface of an isolated uniform solid sphere of mass M and radius R is found to be V A spherical cavity having radius R 2 is created inside the sphere which is touching the surface of original sphere The cavity is then filled with material having density 16 times that of original sphere A B C and D are consecutive points as shown in the figure each R 2 apart V V V and Vare gravitational potentials found at points A B C and D respectively 82 82 82 Column I A V B V CV D V q r 18 7V 13 4V 19 4V 21 4V 25 4 Column II

D The density of core of a planet is p and that of the outer shell is p The radii of core and that of the planet are R and 2R respectively Gravitational acceleration at the surface of planet is same as at a depth R Then value of is P P2 a 2 3 b 4 5 c 3 2 d 5 4

Weight of an object on earth s surface is 200 kg wt Then find out its weight on the surface of planet having mass 1 of earth and radius half of the times 4 earth Question Type Single Correct Type 1 100 kg wt 2 200 kg wt 3 300 kg wt 100 ka wt

Pre Medical Physics Following curve shows the variation of intensity of 13 A N gravitational field 1 with distance from the centre of solid sphere r 3 111 O O R R I FIM 12 Suppose the acceleration due to gravity at the earth s surface is 10m s and at the surface of mars it is 4 0 m s A 60kg passenger goes from the garth to the nchin moving with a r

2 Two satellites S and S revolve around a planet in coplanar circular orbits in the same sense Their periods of revolution are 1 hour and 8 hour respectively The radius of the orbit of S is 104 km When S is closest to S the speed of S relative to S in km h 2 2 a 104 c 105 b x 104 d x 105

Question 31 If a body of mass m is taken out from a point below the surface of earth equal to half the radius of earth R to a height R above the earths surface then work done on it will be O a 5 6 mgR O b 6 7 mgR O c 7 8 mgR O d 8 9 mgR

A block is placed on the top of a fixed smooth sphere as shown and given a slight push so it starts moving on sphere What will be the acceleration in m s of block just after it leaves the contact from sphere g 9 8 m s

Two small spheres each having a charge Q are suspended by insulating threads of length from a hook This arrangement is taken to a space where there is no gravitational effect the the angle between the two threads and the tension in each will be 1 180 1 Q 4 2L 1 Q 2 90 3 180 1 Q 4 21 2 4 E L 4 180 1 Q 4TE L

A body on earth s surface is at a latitude of 60 N Consider only rotation of earth about its own axis then Take Earth s radius 6400 km A Centripetal acceleration of body is 0 017 m s B Centripetal acceleration of body is 0 034 m s C Centripetal acceleration of body is 1 m s D Centripetal acceleration of body is 9 8 m s

the earth around the sun is 1 5 x 108 km 8 14 A saturn year is 29 5 times the earth year How far is the saturn from the sun if the earth is 1 50 x 108 km away from the sun Non the surface of the earth What is the gravitational force on it

Determine the inductance per km per phase of a single circuit 460 kV line using two bundle conductors per phase as shown in Fig E 2 7 The dia of each conductor is 5 0 cm 40 cm a a 6 5 m Fig F 27 b 6 5 m O c

he average distance of the sun from a planet is 9 times in comparison om earth Find the time period of revolution of the planet tance of a planet from the sun is four times the distance of earth from the sun Period of to average dista UPB 2014 An

earth having radius en due to gravity is 2016 11 R R arth v to the ose radius and 15 A satellite S is moving in an elliptical orbit around the earth The mass of the satellite is very small compared to the mass of the earth Then 2015 Re a The acceleration of S is always directed towards the center of the earth b The angular momentum of S about the center of the earth changes in direction but its magnitude remains constant c The total mechanical energy of S varies periodically with time d The linear momentum of S remains constant in magnitude 16 Dependence of intensity of gravitational field E of earth with distance r from center of earth is correctly represented by 2014