Gravitation Questions and Answers

Consider two solid spheres of radii R Im R 2m and masses M and M respectively The gravitational field due to sphere 1 and 2 are shown The value of Gravitational field E 2 1 1 2 2 M M is 0 1 2 3 4 5 radius R 2

great height 8 A is a above the hole in the earth dug along its diameter a The motion of the particle is simple harmonic b The motion of the particle is periodic 3

Q 17 A body is projected vertically upwards from the surface of earth with a velocity sufficien enough to carry it to infinity The time taken by it to reach height h is S ptions 1 2 3 12Re 31 g TH Re 2g Re 3 2g 1 12R 1 C 1 h Re 1 h Re h 2 h Re 3 3 1 2 2 13 3 2 1 1

At a smooth horizontal table are two identical cubes of mass m connected by a spring of rigidity k The length of spring in the unstretched state is lo The right cube is linked to the load mass m at the end At some time the system is released and the system moves without initial velocity Find the maximum distance in cm between blocks during the motion of the system Pulley is smooth string is light inextensible Table is long so that no blocks hits pulley the suspended mass does not have floor below it g 10 m s lo 1 cm m 3 kg k 1000 N m m m vooooooooo

20 A satellite of mass m revolves around the earth of radius R 20 m at a height x from its surface If g is the acceleration due to gravity on the surface of the earth the orbital speed of the satellite is 1 gx gR 2 R X 3 GR R X 4 GR 74 2 R x fon F conut 1 gx gR 2 R x 3 GR R x 4 74 2 gR R x COOLTE for ateriat 20 i T

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

orrectly represents the ratio gi d go a X2 p 6 p 6 X 4 p 6 p 6 p 6 p 6 p 6 p 6 1 25 1 00 0 75 0 50 0 25 0 00 1 00 0 75 0 50 0 25 0 00 0 00 1 25 1 00 0 75 X3 0 50 0 25 0 00 1 25 1 00 0 00 0 25 0 50 d R 0 75 0 50 0 00 0 25 0 50 d R 0 25 0 00 0 25 0 50 0 75 1 00 1 25 d R 0 75 1 00 0 00 0 25 0 50 0 75 1 00 0 75 1 00 24 30

1 The magnitude of the gravitational force experienced by a small spaceship of mass M inside an inter galactic dust cloud assumed to be spherically symmetric but not necessarily uniform when it at a distance of r from the center of the cloud is found to be The density of the dust cloud is G is Newton s gravitational constant 3a A 4GM 1 3 B 1 2 3c 4 GM C GM 1 4 GM D B F r ar r 3a AUGM

34 Three corners of a square have charges 1 2 5 esu What charge should be placed on the fourth corner so that the potential at the centre of the square is zero A 4 esu B 3 esu C 4 esu D 3 esu 35 Two equal masses m are moving in a circle of radius R under the influence of their mutual gravitational attraction The velocity of each mass is A Gm 4R B Gm R C G mR D GR m

5 Four particles each of mass m are placed corners of a square of side a The potentia centre of square will be 1 Zero 2 4 2 Gm a 3 2 Gm a m m 3 3

A ball of mass m is thrown vertically upward in air The time of ascent is t and time of descent is ta air resistance is taken into account Choose the correct statement A ta ta B ta ta

Two satellites Si and S2 revolve round a pla the same direction in circular orbits periods of revolutions are 1 hour and 8 rospoctively The radius of Sy is 10 km radius of S2 will be 1 4 x 104 km 3 2xx 104 km 2 104 km 4 104 km 2

The escape velocity from the Earth s surface is u The escape velocity from the surface of another planet having a radius four times that of Earth and same mass density is 1 3 v GM g 2 4 v 3 U R2 GM 44R G 2 16

If I go above the Earth s surface and sta y at a fixed point for more than 12 hour s and than come back to Earth s surfac e very fast in approximately few minute s than will I find me at a different plac e

A person of mass 80 kg jumps from a height of 1 m and foolishly forgets to buckle his knees as he lands His body decelerates over a distance of only 1 cm During deceleration the total force on his legs is g 10 m s A 800 N C 8080 N B 880 N D 80800 N

A body of mass m and radius r falls on earth from a great height If M is mass and R is the radius of earth while Rthen the acceleration of the body when it hits the 100 earth is acceleration due to gravity at earth surface is g a g c d 9 8g b 0 98 g

Two identical spheres of mass M and radius R are held fixed and separated by a distance D A small projectile of mass m is fired with initial velocity V from the surface of one sphere directly towards the other The projectile is attracted gravitationally by each sphere and no other forces are acting Which of the following graph best represent the potential energy U x of the projectile as a function of distance x from the centre of the sphere on the left measured along the axis between the two the spheres 3 U x U x U x U x A X B X C X D ic X

A satellite moves in a circle around the earth The radius of this circle is equal to one half of the radius of the moon s orbit The satellite completes one revolution in 1 113 la alm 2 2 2 lunar month lunar month 3 23 2 lunar month 4 23 2 lunar month

A particle rests on the top of a hemisphere of radius R Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down 1 3 gR VER 3gR 2 2gR 4 5gR

A tunnel is dug across the earth along a chord AB as shown A particle is projected inside the tunnel from end A with an initial velocity vo 3g R 2 there is no friction between the tunnel and the particle Then choose the correct option s where go gravitational acceleration on the surface of Earth R radius of earth B Vo Ve 30 R 3g R 2 A A The time taken by the particle to move from end A to other end B of the tunnel is R 3 19 B The time taken by the particle to move from end A to other end B of the tunnel is 2 R 3 9 C The maximum speed of the particle inside the tunnel is gR D The maximum speed of the particle inside the tunnel is 2g R

4 60 A coil in the shape of an equilateral triangle of side 0 02m is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of a permanent magnet producing a horizontal magnetic field of 5 10 2 tesla Find the couple acting on the coil when a current of 0 1 ampere is passed through it and the magnetic field is parallel to its plane Ans 8 66 x 10 7Nm

With what velocity should a particle be projected 32 Is from the surface of earth so that its maximum height from surface of earth becomes equal to radius of earth if R Radius of earth M Mass of earth 1 3 GM R 2GM R The additional kinatio 2 4 8GM R 4GM R Asked by 3310898 aesl id Standard XII Stream NEET Jul 26 2021 at 8 12 PM Add your responses Type Text Type your answer here OR you can upload an attachment from the option below

Largest and smallest distance of a satellite from center of planet are given by Rmax and Rmin respectively At these two positions speeds are given Vmin and Vmax respectively The time period of revolution of the satellite is T If a and b are semi major and semi minor axis then a O b VRmax Rmin a Rmax Rmin 2 b T 2T T VmaxVmin V Vmin

The variation of the gravitational potential V for the uniform solid sphere of mass M and radius R with distance r from the centre is bes represented as IM R M R LA 4 M R IM Read More

35 Acceleration due to gravity in a planet having same shape compared to the Earth but two greater density than earth will be acceleration due to gravity in earth surface is 9 8 m s A 19 6 m s B 9 8 m s C 0 m s D 4 9 m s

Fo 7 A satellite is revolving on a circular path round a planet of mass M at a distance R OP from its centre O When satellite is at point P by some internal mechanism its velocity is change to vector V PQ Choose the correct option s P

Three identical bodies of equal mass M each are moving along a circle of radius R under the action of their mutual gravitational attraction the speed of each body is 1 3 GM R GM 3R 2 4 GM 3R GM 2R

Two satellite are revolving around the earth in the circular orbit of radius 2R and 8R with same sense of rotation At t 0 centre of earth lies on the line joining the centres of satellite Ther minimum time after which all three centre lies on the same line again M Mass of earth 1 3 4T R 7 GM 16A 2R 7 GM 2 4 T R 7 GM R GM

A second s pendulum is placed in a space laboratory orbiting around the earth at a height of 3R where R is the radius of earth The time period of the pendulum is 1 Infinite 3 4 s 2 Zero 4 2 3s 8

A clock P is based on oscillation of a spring and another clock Q is based on pendulum motion Both the clocks run at the same rate on Earth Both the clocks are then taken to a planet having same density as Earth but twice the radius Then 1 P will run faster than Q 2 Q will run faster than P 3 Both will run at the same rates as on Earth 4 Both will run at equal rates but faster than on earth

An object is dropped from rest above the surface of a planet and it falls 13 5 meters in 3 seconds The radius of the planet is 5 82 10 6 m What is the mass of the planet 1 52x10 24 Kg 3 04x10 24 Kq 4

9 The gravitational field in a region is given by E 41 N kg Work done by the field is zero if particle is move along the line 1 y 4x 2 3 x y 5 PAEZT 4y x 6 4 x 2y 4 X

A tunnel is dug across the diameter of earth A ball is released from the surface of Earth into the tunnel The velocity of ball when it is at a R distance from centre of earth is where R 2 radius of Earth and M mass of Earth 1 3 3GM 4R GM an 2 2GM V 3R 2GM

The gravitational force between two bodies of mass 2m each separated by a distance r is F For two different pair of bodies of mass m each separated by a distance r 2 this for ce becomes D Find F D

Two stars each of mass M and separated by a distance orbit about their centre of mass A planetoid of mass m m M moves along the axis of this system perpendicular to the orbital plane Let T be the period of simple harmonic motion for the planetoid for small displacement from the center of mass along the z axis and let T be the period of motion for the two stars T Determine the ratio T A The ratio of T T 2 T C The ratio of T 1 2 2 B The ratio of D The ratio of m T T 12 13

4 Zero 5 The density of a newly invented planet is twice that of earth The acceleration due to gravity at the surface of the planet is double that at the surface of earth If radius of earth is RE then the radius of the planet would be NCERT Pg 190 NOTRE 2 AL RE 2 3 2RE 4 4RE For a satellite moving in a circular orbit 1 6 hours 6 2 hours 6 3 hours 2 4 12 hours 19 A particle is velocity v The velocity of

3 9 O r R V4 9 25 O r R 13 A body weighs 90 N on the surface of earth The gravitational force on it due to earth at a height equal to half the radius of earth is NCERT Pg 190 40 N 1 81 N 3 45 N 14 The escape speed of a projectile on the north surface is 112 km s A body is 4 30 N 16 For a satelli around the ea to the magnit 1 1 3 2 17 A point mass shell of m gravitational mass is

The change in gravitational potential energy when a body of mass m is raised to height 4RE from the earth surface is RE is radius of earth NCERT Pg 192 1 mgRE 3 2 mgRE mgRE 5 4 3 LAT mgRE 5 The potential energy of a system of four

If the gravitational potential at the surface of earth is Vo then potential at a point at height equal to radius of earth is NCERT Pg 192 1 Vo 3 0 Vo 4 15 N 5 V

body is launched 4 All of these A planet of mass m revolved around the sun of mass M in an elliptical orbit The maximum and minimum distance of the planet form the sun are r and 3r respectively The time period of the planet is proportional to TNCERT Pg 184 1 3 J2 27 2 3 4r 4 4r Two point masses m and 9m are separated 5 new force of gravitati y 10 mN 30 3 mN 4 Three equal masses c at the vertices of an ec The gravitational force placed at the centroid X1 Zero 2 6 67 x 10 N

Two point masses m and 9m are separated by a distance d on a line A third point mass of 1 kg is to be placed at a point on the line such that the net gravitational force on it is zero m O 9m The distance of 1 kg mass from mass m is INOM 4077 6 2 6 67 x 10 N 3 9 10 9 N 4 Data is insuffic An object is proje with speed half of then maximum 1 16 RE 2

KEPPLER S LAWS The figure shows elliptical orbit of a planet m about the sun S The shaded area SCD is twice the shaded area SAB Ift is the time for the planet to move from C to D and t is the time to move from A to B then a t 4t b t 2t d t t B

Attempt All 35 questions If R is radius of earth then find the escape speed at a distance R above earth s Surface g acceleration due to gravity O VgR gR V2 VgR 2

Attempt All 35 questions Find the height from Earth s surface where gravitational field is equal to the gravitational field at mid point of Earth s radius 0 5R 0 4R R

Two very long identical skew perpendicular rods of linear mass density are separated by a finite distance d Then A Gravitational force of attraction is finite B Gravitational force of attraction is independent of d C Gravitational potential energy of interaction between the rods is finite D Gravitational force of attraction is inversely proportional to d

31 A body of mass m is placed on the earth s surface It is then taken from the earth s surface to a height h 3 R then the change in gravitational potential energy is CBSE AIPMT 2002 mgR 2 a mgh R 3 b mgR c mgR d 4 adius

escape 5 The earth is assumed to be a sphere of radius R A platform is arranged at a height R from the surface of the earth The velocity of a body from this platform is fve where ve is its escape velocity from the Ve surface of the earth The value of fis e CBSE AIPMT 2006 a 2 b 1 2 c 1 3 d 1 4

2 The shown set up is released at rest obtain the speed of mass M when it comes out of the shell of mass 2m Assume all collisions to be elastic A B C D 2 GM 3 R 2 GM 3 R 8 GM 3 R 2GM R 3 Small opening Large distance 2M

3 67 A chain AB of length is loaded in a smooth horizontal tube so that its fraction of length h hangs freely and touches the surface of the table with its end B At a certain moment the end A of the chain is set free with what velocity will this end of the chain slip out of the tube Ans 2gh In

Solvelancer Test The proportionality constant in the Kepler s law of period is called as Solvelancer Test a There is no proportionality constant Cavendish constant b c Universal gravitational constant Kepler s period constant d