Gravitation Questions and Answers

An artificial satellite of mass m is moving in circular orbit at a height equal to radius R of earth Suddenly due to internal explosion the satellite breaks into two parts of equal pieces One part o satellite stops just after explosion The increase in mechanical energy of system due to explosion wil be 1 mgR mgR 2 4 mgR 2 3mgR

If earth is supposed to be a sphere of radius R if 930 is value of effective acceleration due to gravity at latitude of 30 and g at the equator the value of g 930 is w is angular velocity of rotation of earth 1 1 R 4 3 R 2 4 3 w R w R

A geostationary satellite is orbiting the earth at a height of 5R above that surface of the earth R being the radius of the earth The time period of another satellite in hours at a height of 2R from the surface of the earth is AIPMT 2012 1 6 2 6 2 2 3 5 4 10

3 Three masses each equal to M are placed at the three corners of a square of side a The force of attraction on uni mass at the fourth corner will be 1 3 GM 3a 3GM 2 2 GM3 2 a 4 GM 1 2 2 a 2

A distance of 1 0 meter separates the centers of two small charged spheres The spheres exert gravitational force Fg and electrostatic force Fe on each other If the distance between the spheres centers is increased to 4 0 meters the gravitational force and electrostatic force respectively may be represented as Fg 9 and Fe 9 O4Fg and 4Fe OFg 4 and Fe 4 OFg 16 and Fe 16

uestion No 9 Three solid spheres each of mass m and radius R are released from the position shown in fig The speed of any one sphere at the time of collision would be d G 1 3 Gm R

Acceleration due to gravity on moon is 1 of the acceleration due to gravity on earth If the ratio of densities of 6 Pe 5 Pm earth p and moon pm is then the radius of moon R in terms of Re will be 1 5 Re 18 3 R 2 4 6 Re 1 2 3 3

special theory of relativity was 1 2 3 The time period of any event in every frame of refrance will be the same Speed of light will be constant for all frames of reference For observers all laws related to physical phenomenon are different in different inertial reference frames

A ball is dropped Tro a sal lite revolving around the earth at a height of 120 km The ball will 1 Continue to move with same speed along a straight line tangentially to the satellite at that time Continue to move with the same 2 speed along the original orbit of satellite

8 A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet The maximum height attained by the body is a R 5 6 R 4 b R 2 d R 3 C

The escape velocity from a planet is ve A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface When the body reaches the centre of the planet its speed will be Am 0 1 yd 0 1 vd 259 is a a vedlitw coitomi 6 love 201 Ve c 12 V

A box weighs 196 N on a spring balance at the north pole Its weight recorded on the same balance if it is shifted to the equator is close to Take g 10 ms at the north pole and the radius of the earth 6400 km 1 195 66 N 3 194 32 N 2 194 66 N 4 195 32 N

It is Meech Lake all over but the talks are conducted on a hot air balloon that rises from rest with an acceleration of 1 1 m s due to the heated discussions Fifty seconds into the thermal talks Loosened Bouchard has had enough and jumps out of the balloon with an initial vertical speed of 3 0 m s upwards relative to the balloon causing a massive uproar Jea Chr tien who was not aloud on the top deck seeing that the Loosened Bouchard forgot his Fleur De Leap Jetpack throws the Bombardier Jetpack straight down two seconds after th fateful jump which the grateful Bouchard catches eight seconds after his jump What was the speed of the jetpack relative to the balloon when it was thrown downward Answer in m s Jean Chr tien Meech Lake Loosened Bouchard Bombardier Jetpack Accord

i For a low altitude orbit ifrrp where rp is planet radius show that for a given average planetary density the orbital period of satellite is independent of the size of the planet Calculate its value if average density is p 3T Go Gp

Three equal masses of 3 kg each are fixed at the vertices of an equilateral triangle ABC The gravitational force acting on mass 2 kg placed at the centroid of triangle is NCERT Pg 187 1 Zero 2 6 67 x 10 N 3 9 10 9 N 4 Data is insufficient

The force of gravitation between two mas is 10 mN in vacuum If both the masses are placed in a liquid at the same distance ther new force of gravitation will be NCERT Pg 187 1 10 mN 30 3 mN 2 40 3 mN 4 Can t say

6 23 Two satellites S and S revolve round 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 The speed of S relative to S when they are closest in kmh is A 104 T C 10 T B 2 104 T tudi dous D 4 10 T

in a direction making vi A particle is projected from point A that is at a distance 4R from the centre of the Earth with speed v 30 with the line joining the centre of the Earth and point A as shown Find the speed v of particle if particle passes grazing the surface of the earth Consider gravitational interaction only between these two GM Use 6 4 107 m s R A 4R R 30 V Figure 6 88

6 48 A hole is drilled from the surface of earth to its centre A particle is dropped from rest at the surface of earth The speed of the particle when it reaches the centre of the earth in terms of its escape velocity on the surface of earth v is e Ve A 2 2 C 2v B ve D 2 La

iv Two small dense stars rotate about their common centre of mass as a binary system with the period 1 year for each One star is of double the mass of the other and the mass of the 1 lighter one is of the mass of the Sun Find the distance 3 between the stars if distance between the Earth the Sun is R R be V ra

Two bodies of masses M and M2 are kept separated by a distance d The gravitational potential at a point where net gravitational field intensity by them is zero is C M M M 2 M M M M 2 JM M GM M M M d G M M 2d

An earth of mass orbits along along a circular orbit C at a height 2R from earth s surface It is to be transferred to a circular orbit C of bigger radius at a height 5R from earth s surface The transfer is affected by following an elliptical path as shown in figure Calculate the change in the energies required at the transfer points A is R radius of earth mgR 36 mgR 18 SR 2R C a mgR 2 mgR 9

1 10 V 2 15 V 3 20 V 4 30 V How high a man be able to jump on the surface of a planet of radius 320 km but having density same as that of the earth if he jumps 5m on the surface of the earth Radius of earth 6400 km 1 60 m 2 80 m 3 100 m 4 120 m

S The acceleration due to earth s gravity on a point particle at a height h above the surface of th earth is denoted by g h and at a depth d below the surface of the earth is denoted by gi d Consider the earth to be a sphere of radius R with uniform mass density Which of the followin correctly represents the ratio gi d go d X 1 2 X 3 X 4 p 6 p 6 p 5 p 6 1 25 p 6 p 6 1 00 0 75 0 50 0 25 0 00 p 6 p 6 0 00 1 25 1 00 0 75 0 50 0 25 1 00 0 00 0 00 0 25 0 50 0 75 1 00 d R 0 75 0 50 0 25 0 00 0 00 0 25 0 50 1 25 1 00 0 75 0 50 0 25 0 50 d R 0 25 0 00 0 75 1 00 0 75 1 00 1 25 d R

6 A jet airplane travelling at the speed of 500 km h ejects its products of combustion at the speed of 1500 km h relative to the jet plane The speed of the products of combustion with respect to an observer on the ground is a 500 km h c 1500 km h On a long horizontally b 1000 km h d 2000 km h moving belt a child runs to

How much energy will be necessary for making a body of 500 kg escape from the earth g 9 8 m s radius of earth 6 4 x 106 m Question Type Single Correct Type 1 About 9 8 x 106 J 2 About 6 4 108 J 3 About 3 1 x 1010 J A About 274 x 1012 I

Assume that the Earth changes its shape and turns into an infinite cylinder whose radius and density are the same as those of our real Earth and the distance of the Moon from the central axis of this cylindrical earth remains unchanged What can you say about the speed of the Moon which remains spherical in its orbit around the cylindrical Earth a It will slightly increase c It will remain unchanged b It will slightly decrease d It will increase several times

I want to know why while applying co nservation of mechanical energy we have taken the potential energy of th e final state but not of the initial stat e that should be kQe b Also How torque about nucleus is zero A nd how mv b mv r where does this relation comes from 106 Electrostatic Potential and Capacitance Example 8 Solution Board Competitive Exams Le An electron mass m charge e is moving towards a heavy nucleus of charge Q fixed at t place When the electron is far from the nucleus its speed is vo and the impact parameter is b What is the closest distance of the electron from the nucleus or 1 The path of the electron is shown r is distance of closest approach v is the speed at this Pasell instant Clearly v is perpendicular to radial distance The angular momentum of electron about the nucleus remains conserved as torque about nucleus is zero mvb mvr Also by conservation of mechanical energy mv my 2 Vob To 2Qe v 4TE mr 2 v 1 Q e v b v r 4 eo To 2Qe 4 E mr 2Qe 4 em 2Qe ro v b 0 4 m ro Vob 1 ii b V Boa B 4

The relative uncertainty in the period of a satellite orbiting around the earth is 102 If the relative uncertainty in the radius of the orbit is negligible the relative uncertainty in the mass of the earth is 1 2 x 10 2 6 x 10 3 3 x 10 2 4 10

estion No 21 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 s1 The change in kinetic energy when it has ached 5 x 109 m away from sun is velocity and position vector of comet is perpendicular to each other at both instant 032 107 J O 2 4 x 10 J O 2 5 x 10 3 J O 48 10 2 J

MO M A D GM D B GM 2D C v GM D D v MGD E D 2GM D Obta 20 Two identical stars a fixed distance D apart revolve in a circle about their mutuai center of mass as shown above Each star has mass M and speed V G is the universal gravitational constant Which of the following is a correct relationship among these quantities

A 70 kg astronaut is repairing spaceship at a height of 640 km above the surface of earth His weight at that location is nearly g 10 m s 460 N 490 N 580 N

Two bodies of masses M and M are kept separated by a distance d The gravitational potential at a point where net gravitational field intensity by them is zero is M M 2 M M M M 2 JM M GM M M M d G M M 2d

37 The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B A man jumps to a height of 2 m on the surface of A What is the height of jump by the same person on the planet B a 2 9 m b 18 m c 6m d 2 3 m 2003

Figure shows a binary star system revolving about their COM The masses of star A B are 15 x 100 kg and 45 x 1030 kg respectively Find the ratio of area swept by star A to area swept by star B in a common time interval B COM

4 Friction is acting downward and static in nature 1 Two satellites are in the parking orbits around the earth Mass of one is 10 times that of the other The ratio of their periods of revolution is 1 1 2 10 4 10 10 3 1 10

The density of a soud spherical planet of radius R is given as p pol where po constant and r is distance measured from centre of planet The acceleration due to gravity of this planetas half of maximum value at distance x from centre and also at a distance y from the centre The value of x y is R Here a and p are single digit integer Find the value of 0 87

Four point masses each of mass m are placed on vertices of a regular tetrahedron Distance between ar two masses is r A Gravitation field at centre is zero B Gravitation potential at centre is 4Gm r C Gravitation potential energy of system in 6Gm r D Gravitation force on one of the point mass is 6Gm

26 Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T If the gravitational force of attraction between the planet and the star is proportional to R 5 2 then 72 is proportional to a R c R3 2 b R712 d R9 2

joule second A metal plate is kept stationary and normally ina time varying magnetic field then 1 Both emf and current are induced in the mea plate 2 A current but no emf is induced in the metal plate 3 An induced emf but no current is induced in the metal plate 4 Neither induced emf nor induced current is induced in the metal plato

3 A solid sphere of mass M and radius R has a thin groove cut along the diameter as shown in the figure This rod of length 2R mass per unit length is placed in the groove A 3GM V2R a Rod perform SHM only if x R with an angular frequency of o b The rod perform oscillatory motion but not SHM with an angular frequency of GM R c Rod perform SHM only if x R with an angular frequency of 0 GM R 2GM d Rod perform SHM only if x R with an angular frequency of VR

45 In gravity free space a thin spherical shell of mass M and radius Ris held fixed There is a small hole in the shell A small mass m is released from rest at a distance R 4 from the hole along a line that passes through the hole and also through the centre of the bshell The time taken by the particle to travel from the hole to the point diametrically opposite is a 2r R GM 10R3 b m me R 4 M c 2R3 d 3R3

Three stars each of mass m rotate in a circle of radius r with uniform angular speed unde mutual gravitational attraction The angular speed of each star is A B C 3Gm 3 Gm D Gm 3r 3Gm 3

While discussing the variation of g or the ac celeration due to gravity for the variation of depth we are considering that the inner shel Is of the earth are responsible for the value g Why aren t we considering the outer shell s as they are also attracting the object

29 If the angular velocity of a planet about its own axis is halved the distance of geostationary satellite of this planet from the centre of the planet will become a 2 1 3 times b 2 3 2 times d 4 times c 2 2 3 times 0 18 6

Example 17 An electron falls through a distance of 1 5 cm in a uniform electric field of value 2 x 104 N C When the direction of electric field is reversed a proton falls through the same distance Compare the time of fall in each case Contrast the situation with that of free fall under CBSE 2018 C gravity

On to a sphere of radius R 2 and density p2 with centre at C a second solid sphere is moulded with density p radius R and centre C Find the force experienced by a point mass m at point P at a distance y from the combination as shown P1 Pom y R Ci P2 C R 2

21 If the radius of the earth were increased by a factor of 2 keeping the mass constant by what factor would its density have to be changed to keep g the same a c 8112 b 4 d 1 4 odigd wolled A E

45 The gravitational potential of two homogeneous spherical shells A and B separated by large distance of same surface mass density at their respective centers are in the ratio 3 4 If the two shells coalesce into single one such that surface mass density remains same then the ratio of potential at an internal point of the new shell to shell A is equal to a 3 5 b 4 5 c 5 3 d 5 4

50 A small section of area AA is removed from a uniform spherical shell with surface mass density o and radius R as shown in the figure Find the magnitude of gravitational field intensity at point P due to the remaining mass 40AAG 9R2 GAAG R Sarj c P O R 2 R b AA 40AAG R d zero