Gravitation Questions and Answers

7 Two satellites X and Y revolve in the same circular orbit around the earth The mass of X is greater than the mass of Y Which of the following is greater for X then Y 1 Speed only 2 Speed and gravitation force only 3 Potential energy and gravitation force ray and gravitation force

E 6 28 Two bodies of masses m and M are placed a distance d 6 apart The gravitational potential at the position where the gravitational field due to them is zero is V B V G A V m M d lanet in C V of revol d Gm d G 2 D V m M d

O An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth Determine the gain in the potential energy of the object 1 Obtain the expression for gravitational potential and field due to a solid sphere at

2 For an object lying on the surface of the Earth the Escape speed is 11 2 km s If an object on the Earth is thrown away with a speed three times this value find its speed after it has escaped from the gravitational field of the earth a 42 69 km s c 29 63 km s b 31 63 km s d 19 23 km s

around the sun twice as fast as the earth What would be its orbital size as compared to that of the earth lo one of the satellites of Jupiter has an orbital period of 1 769 days and the radius of the orbit is 4 22 x 10 m Show that the mass of Jupiter is about one thousandth that of the sun

2 4 A rocket is fired from earth s surface with a 10 speed v 2 Rg in the upwards direction Z 1 The rocket will remain in earth s gravitational field 2 The rocket will revolve round the earth 3 The rocket will escape from the earth 4 None of the above 4 2 3 4 3 Z v 2 4 4 fenfu f 1 tequil Jord U T M 2 ga sir for A

mass 2M is attached to a massless spring Wi spring constant k This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings and The acceleron of the blocks are a 9 the figure The system is released from rest with the spring in a as shown in its unstretched state The maximum extension of the spring is xo Which of the following option s is are correct g is the acceleration due to gravity Neglect friction 2M M b Xo 93 XO a At an extension of of the spring the magnitude of 4 4Mg k 2M 3g acceleration of the block connected to the spring is 10 Xo c When spring achieves an extension of 2 for the first time M the speed of the block connected to the spring is 3g 5k

placed at vertices of an equilateral triangle of arm L keeping the triangle as such by which angular speed the bodies should be rotated in their gravitational fields so that the triangle moves along circumference of circular orbit 1 2 3 3GM L3 GM L GM 3L3 are GM

The density p of a sphere of radius R varies with distance r from the centre as p po 1 The gravitational field is constant The gravitational field at r Ris 5 GR 6r The gravitational potential on the surface is 13 GR 24 The gravitational field at r RQ is 5 GR 6 2 The 2R

A spherically symmetric gravitational system of particles has a mass density Poforr SR Oforr R where Po is a constant A test mass can undergo circular motion under the influence of the gravitational field of particles Its speed V as a function of distance r 0 r from the centre of the system is represented by 2008 a c R V r b d R 4 R

A marble of radius r rolls back and forth without slipping in a spherical dish radius R Use energy considerations to show that the motion is simple harmon for small displacements of the marble from its equilibrium position and dedu an expression for the period of the oscillations The moment of inertia I o solid sphere of mass m about an axis through its centre is equal to mr

Question 6 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 height R above the earths surface then work done on it will be a 5 6 mgR b 6 7 mgR e 7 8 mgR d 8 9 mgR

A particle of mass m is thrown in a parabolic path towards earth having mass M and radius R It comes to a greatest approach distance R 2 from surface of earth Magnitude of total energy change required to make the particle moving in an elliptical path having eccentricity 1 2 with the greatest approach point either aphelion or perihelion are 0 0 O 1 GMm 3 R 1 GMm 6 R 1 GMm 2 R GMm R 4

Two identical particles of mass M and charge Q are placed at same distance If they are in equilibrium under gravitational and electric force then calculate value of Q M is B C 0 1 4TEOG 4TEOG rG K G

10 A satellite is moving in circular orbit with areal velocity V If the radius of the earth is R and the acceleration a due to gravity on the surface of the earth is g then the altitude H at which the satellite is orbitting is K P fiv 1 2 3 4 V a 2gR a V gR 2V gR 4V R a R R gR a R mari at much kat kt 27 2 2 7x 31

3 4 6 When a planet moves around the Sun a its angular momentum about the sun remains constant b it moves faster when it is nearer to the Sun c its total energy increases when it goes nearer to the Sun d its potential energy decreases when it goes nearer to the Sun The correct statements are 1 a b c 3 a d c 2 b c 4 a b d

satellite of Mars called Phobos has an orbital radius of 9 4 x 106 m and a period of 2 8 x 104 s Assuming the orbit is circular determine the mass of Mars kg

satellite is in a circular orbit around the Earth at an altitude of 3 32 x 100 m a Find the period of the orbit Hint Modify Kepler s third law 72 m 4x GMS so it is suitable for objects orbiting the Earth rather than the Sun The radius of the Earth is 6 38 x 106 m and the mass of the Earth is 5 98 x 1024 kg b Find the speed of the satellite km s c Find the acceleration of the satellite m s2 toward the center of the earth

2 Set both masses to 5 00 billion kg and the distance between them to 3 00 km What is the magnitude of the gravitational force between the two masses

Will is a scien igning Will knows that the gravitational pull of Mars is less than the gravitational pull of Earth When he lands on Mars his mass will be weight on Mars will be his weight on Earth

Two ships of equal mass are 103 m apart What is the acceleration of either ship due to the gravitational attraction of the other Treat the ships as particles and assume each has a mass of 39 000 metric tons Give the magnitude of your answer in m s m s

Solve the following variance problem Kepler s third law of planetary motion states that the square of the time required for a planet to make one revolution about the sun varies directly as the cube of the average distance of the planet from the sun If you assume that Mars is 1 5 times as far from the sun as is the earth find the approximate length of a Martian year

10 A satellite is in a circular orbit around an unknown planet The satellite has a speed of 2 35 x 10 m s and the radius of the orbit is 5 65 x 100 m A second satellite also has a circular orbit around this same planet The orbit of this second satellite has a radius of 8 70 x 100 m What is the orbital speed of the second satellite m s

7 A 200 kg satellite is in circular orbit at a height of 600 km above the earth s surface a Find the speed of the satellite A 2 b Find the gravitational field strength at this altitude A 2

ents Two particles A and B of masses mand 2m respectively are released from rest from separation 2r They move under Find n mutual gravitational attraction The speed of particle A when their separation decreases to r is n Gm 3r Answer 00 01 02 00 01 02 Select your answer from radio buttons 03 0 3 04 04 05 0 5 06 06 07 07 08 08 09 09

A satellite m 800 kg is launched to a medium Earth orbit MEO having an altitude of two Earth radii RE 6378 km a Derive the equation for the work the gravity does on this satellite during the launch and calculate the numerical value for that b The satellite enters the MEO orbit and makes uniform circular motion around the Earth What is the work done by the net force when the satellite makes one round around the Earth

Potential at the centers of two very thin spherical shells A and B of equal radii and equal masses are VA and VB respectively Mass of shell A is uniformly distributed whereas distribution of mass on shell Bis non uniform Potential at infinity is zero then

3 8 cm 4 13 2 cm 16 At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Eargh s atmosphere Given Mass of oxygen molecule m 2 76 x 10 26kg Boltzmann s constant k 1 38 10 23 J K 1 5 016 104 K 3 8 360 x 104 K 2 1 254 x 104 K 4 2 508 104 K Th

184 A satellite revolving around equator is seen after every 6 hour at a place on equator If the satellite revolves opposite to that of earth s rotation then the angular velocity of the satellite about the centre of the earth in radian hour is 2 T 1 3 TC TL TC

To su p 51 Which of the following graphs closely represents the variation in kinetic energy of a planet as it moves once round the sun in its elliptical orbit t time AM KEA RM 1 2uibs1 bre 2 28smliscA 84 1 Ishoshon s 01 29 o sbutingsm om nentoeage islug KEA ai di 3 VITE KEA 4 Kilos suprat KEA

6 32 Find the ratio of kinetic energy required to be given to satellite to escape from earth to the kinetic energy required to be given to the satellite to revolve sound the earth in an orbi just above the earth surface

6 21 Three masses 100 kg 200 kg and 500 kg are placed at the vertices of an equilateral triangle with sides 10 m They are rearranged by an agent on the vertices of a bigger triangle of sides 15 m and with the same in centre Calculate the work done by the agent Ans 3 77 x 10 7 J

2 The magnitude of change in potential energy of a particle of mass m when it moves from the centre of the earth to the surface of the earth will be 1 mgR 2 3 3mgR 2 4 mgR 4 mgR 2

ce 6 34 Two identical solid spheres each of radius R are placed in its contact with each other It is observed that the gravitational attraction between the two is proportional to R Find the value of n ity he Ans n 4

that the object of mass m escapes from earth s gravitational field v escape velocity 3 2v 45 2 V 4 11 3 v 1 3 2v 45 14 LiD Examy 2 Ve 4 11 3 v

3 00 0 4 1 0 00 Q 118 A satellite of mass m is orbiting the earth of radius R at a height h from its surface The total energy of the satellite in terms of gar the value of acceleration due to gravity at the earth s surface is 2mg R R h 1 3 mg R 2 R h 2 2mg R R h mg R 2 R h FRA 3 09 00 Q 118 m eft hefe geaft PR da ar 1 3 4 0 9 2mg R R h mg R 2 R h 2 4 2mg R R h mg R 2 R h

Q 22 A hollow vertical cylinder of radius r and height h has smooth internal surface A small particle is placed in contact with the inner side of the upper rim at a point P It is given a horizontal speed u tangential to rim It leaves the lower rim at point Q vertically below P the number of revolutions made by the particle will be P A n h 2 r B n u 12gh h C n 2 r h u D n 2pr 2h

15 A bead of mass m is tied at one end of a spring of spring constant k mg R and unstretched length R 2 and other end to fixed point O as shown in the figure The smooth semicircular wire frame is fixed in vertical plane The normal reaction between bead and wire just before it reaches the lowest point is N Find the ratio of N to weight mg of the bead Radius of semicircular frame is R A 6 B 6 25 R H K mg R R 21 ageegeeeee C 11 2 D 16 co m The rate

Four particles of equal mass M move along a circle of radius R under the action of their mutual gravitational attraction The speed of each particle is A C GM R GM R B 2 2 GM 2 2 1 D R GM 2 2 1 R 4

If a body is projected vertically upward from the surface of earth so as to reach a height nRe above the surface Then Re radius of the earth af yg azg a qed A Ha Gefur f4 G42 gefa fu ga fch us faz 3 z u a m y a Re gea AJUT A n 1 B n 34 Gul 1 mgR Correct Answer Your Answer C Increase in its potential energy is mg Re R D Increase in its potential energy is nmgRe nmg Projection velocity must be equal to 2ngRe n 1 2ngRe n 1 Correct Answer Your Answer car Projection velocity must be gRe getoon La

POE 1 58 A particle moves in the plane x y with constant Tool acceleration a directed along the negative y axis The equation of motion of the particle has the form y k x k x where k and k are positive constants Find the velocity of the particle at the origin of coordinates a Ans 1 2 38 world

54 A car is moving towards a high cliff The driver sounds a horn of frequency f The reflected sound heard by the driver has frequency 2f if v the velocity of sound then the velocity of the car in the same velocity units will be 1 2 3 4 2 4 2 2 2 3

An object of mass 10 kg launched from the Earth s surface reaches the speed of 10800 m s at a very far distance from the Earth Determine the initial launch speed of the object Neglect atmospheric friction and the rotation of the Earth The Earth s radius and mass are 6371 km and 5 972 1024 kg respectively

3 12 A spherical shell of mass M inner radius R and outer radius R is shown in the figure The variation of magnitude of gravitational field intensity as a function of radial distance r from the centre of the sphere is best represented by E P R R R R R 2 4 R R

A satellite is seen each 36h over the equater at a place o n earth when its sense of rotation is same as earth The ti me taken after which it can be seen at some places when sense or rotation Is opposite 3 A satellite is seen after each 36 h over the equator at a place on the earth when its sense of rotation is same to earth surface The time interval after which it can be seen at some place when the sense of rotation of earth and satellite is opposite 2 9 hours 4 24 hours 1 12 hours 3 6 hours

o bodies is where R is n the orbital ar orbit is i 4 1 R GR0077 82 Two identical satellites are at the heights R and 7R from the earth s surface Then which of the following statement is incorrect R Radius of the earth 1 Ratio of total energy of both is 5 2 Ratio of kinetic energy of both is 4 3 Ratio of potential energy of both 4 4 Ratio of total energy of both is 4

nentum atement SSIO81 If a satellite is revolving very close to the surface of GR0080 ssion 202 or I will earth then its orbital velocity does not depend upon 1 Mass of satellite 3 Radius of earth 2 Mass of earth 4 Orbital radius

Two satellites A and B go around the earth in circular orbits at heights of RA and RB respectively from the surface of the earth Assuming the earth to be a uniform sphere of radius R the ratio of the magnitudes of their orbital velocities is A imel C RB VRA Rg Re VR R RB Re B R R up D RA RB 2

34 Geostationary satellite 1 is situated at a great height above the surfa of earth 2 moves in equatorial plane 3 have time period of 24 hours 4 have time period of 24 hours and moves equatorial plane

Dust particles released by comets are continuously acted upon by sun s radiation pressure in radial outward direction Assuming a dust particle with p 3 5 x 10 kg m and reflection coefficient 0 for what value of radius r does gravitational force on dust particle just balance the radiation force on it from sunlight power radiated by sun 4 x 1026 w mass of sun 2 x 1030 kg