Gravitation Questions and Answers

6 71 A particle of mass 1 kg is placed at a distance of 4 m from the centre and on the axis of a uniform ring of mass 5 kg and radius 3 m Find the work required to increase the distance of the particle from 4 m to 3 3 mis G Ans J

In gravitational interaction gravitational field 1 3 dv and potential V are related as I If gravitational potential V verses distance variation is given by Then gravitational field and distance graph is 1 3 usiast Course i 2 A dV dr us frat E Space for Rough Work and for dal 1 anfaa V aufa da fava 1 2 9 r 1001CMG36212000s E H 12082020

the cavity passes through the centre of the sphere as shown in the figure A particle of mass mo is released from centre of cavity choose the correct statement Assume elastic collision R Co Answer A B C Your Attempt Correct answer Gravitation field inside a cavity is uniform Motion of particle inside cavity is periodic motion Motion of particle inside cavity is simple harmonic motion 2a p Rate this question

D 31 Show that critical velocity of a satellite revolving close to the surface of the earth of radius R and mean density p is M 94 61 2R G 3 T The periodic time of linear harmonic oscillator is 2 second with maximum displacement of 1 cm If the particle starts from extreme position find the displacement of particle after seconds 65 9461 0 3

A horizontal overhead power line is at a height of 10 m from the ground and carries a current of 200A from east to west The magnetic field directly below it on the ground will be 1 2 x 10 T south wards 2 2 x 10 T north wards 3 4 x 10 T south wards 4 4 x 10 6 T north wards

A space vehicle destined for Mars was launched into a 200 km circular parking orbit around Earth After coasting for a period of time during which system checks were performed the velocity was increased to 11 386 km s instantaneously This velocity placed the spacecraft on a trajectory that would take it to Mars a What was the speed of the vehicle in the parking orbit b Find e E and h relative to Earth after the velocity increase What kind of orbit trajectory is the interplanetary trajectory c Compare the velocity at 2 000 000 km from Earth with the hyperbolic excess velocity vo Why are they so similar

Suppose that a planet has a surface charge 34 density of electron m given radius of the planet is 8850 km then calculate potential of the planet due to this charge 1 0 16 V 2 160 V 3 0 16 V 4 160 V a 43 1 fit 8850 km 1 0 16 V 2 160 V 3 0 16 V 4 160 V

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 2 f If v is the velocity of sound then the velocity of the car in the same velocity units will be A B D V cole 3 V 4 le 2

A satellite of mass 19 0 kg in geosynchronous orbit at an altitude of 3 58 x 104 km above the Earth s surface remains above the same spot on the gravitational force exerted by the Earth on the satellite Hint The answer is not 186 N

Question No 12 If the earth suddenly contracts to one third of its present size without any change in its mass what will be the ratio of the kinetic energies of the earth after and before contraction

400 km from where Example 10 64 A satellite circled around the earth at a distance of 100 km Determine its orbital velocity if the radiu of the earth is 6400 km and 9 9 8 ms 2 Sol Given radius of earth R 6400 km Distance of satellite from earth h 3400 km Orbital velocity of an artificial satellite can be given as 9 8 64 34 x 105 17 9 VR h v R 64 x 105 1 v 6400 ms

3 The time period of a satellite of earth is 5 hours the separation between the earth and the satellit is increased to 4 times the previous value th new time period will become 2019 a 10 hours c 40 hours b 80 hours d 20 hours

Two bodies of respective masses m and M are placed d distance apart The gravitational potential V at the position where the gravitational field due to them is zero is A V B V C V GIOVIDEO D V m M GM d G m M

6 If the the earth is at one fourth of its present distance from the sun the duration of year will be a half the present year 2020 b c one eight the present year one fourth the present year d one sixth the present year

t of which ONE or MORE THAN ONE is are correct A spherical shell of volume mass density p thickness t and radius R R t is placed concentrically inside another shell of radius 2R having same thickness and of same material as shown in the figure The circumferential stress developed in the outer shell is A compressive in nature C 3GnRtp B Tensile in nature 3 G Rtp 2 2R

8 N number of similar objects of mass t are placed on the vertices of a regular polygon The length of each side of polygon is k If P be the energy by the virtue of motion imparted to one of the particles so that it just escapes the gravitational pull of the system and thereafter kinetic energy Q is given to the adjacent particle to escape then the difference P Q is A NGt2 k B Gt Nk C Gt k D NGt 3k

Two bodies of masses m and m2 are initially at rest placed infinite distance apart They are then allowed to move towards each other under mutual gravitational attraction Their relative velocity when they are r distance apart is A B 2G m m r Correct Answer 2Gm m2 m m r m2

ts At what distance from center of earth the gravitational field strength is 25 of that at the earth s surface given that the radius of earth is R O R O R 0 O 3R 8

Example 2 Sixth A space shuttle while travelling at a speed of 4000 km h with respect to the earth disconnects and ejects a module backward weighing one fifth of the residual part If the shuttle ejects the disconnected module at a speed of 100 km h with respect to the state of the shuttle before the ejection find the final velocity of the shuttle

radius at the entre the ween 54 A binary star system is revolving in a circular path with angular speed w and mass of the stars are m and 4m respectively Both stars stop suddenly then the speed of heavier star when the separation betwen the stars becomes half of initial value is a 2 c Gmw 2 71 3 2 Gmw 5 1 3 b 2 Gm 211 3 5 5 d 2 Gmw 2 11 3 LO 5

40 A particle of mass m is projected upwards with Ve 2 ve escape velocity At highest point velocity v the potential energy of the particle is GMm GMm a c 2R 3GMm 4R b d 4R 2GMm 3R

48 A system cosists of two stars of equal masses that revolve in a circular orbit about their centre of mass Orbital speed of each star is v and period is T Find the mass M of each star G is gravitational constant 2Gv T a V T TG b c V T 2 G d 2Tv3 TG

41 Two particles each of mass mare revolving in circular orbits of radius r 5R in opposite directions with orbital speed vo They collide perfectly inelastically and fall to the ground The speed of combined mass on striking the ground will be 2 2v0 c 2V0 b 2vo d Vo

37 A mass is taken from surface to a height h The change in potential energy in this process is equal to the change in potential energy if it is now taken from that point to infinity What is the value of h b h 2R d h 4R h R 3R c h 2

52 A solid sphere of mass M before cavity and radius R has a spherical cavity of radius R 2 such that the centre of cavity is at a distance R 2 from the centre of the sphere A point mass m is placed inside the cavity at a distance R 4 from the centre of the sphere on the line joining centres of sphere and cavity The magnitude of gravitational pull between the sphere and the point mass m is 14 GMm a 11 GMm R GMm 28 c b d R GMm 4R

18 An engine can pump 25 000 litres of water to a vertical height of 35 metres in 5 minutes Calculate the gravitational potential energy of water at a given height 1 1 71 x 106 J 3 0 28 x 106 J 2 8 57 x 106 J 4 8 57 x 10 J

Eight point masses each of mass m are kept fixed at equal distance on a circle of radius R as shown Now if any one of them is taken very slowly from this position to infinity by performing W amount of work For next time the amount of work performed W upon another point mass which is diametrically opposite to previous one is again taken from its position to infinity very slowly are related as A W W B W W C W W D W W Gm 2R Gm 2R Gm 2R 8 10 R N 3

5 32 A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig 5 19 What is the action on the floor by the man in the two cases If the floor yields to a normal force of 700 N which mode should the man adopt to lift the block without the floor yielding 25 kg 25 kg b

3 1 6 x 10 19 6 25 1012 J Two identical small bodies each of mass m and charge q are suspended from two strings each of length from a fixed point This whole system is taken into an orbiting artificial satellite then find the tension in strings et Tsin 1 2 Kq 12 2 mg 2 2 Kq 2 mg 4 3 2 Kq 2 4 Kq 41 q Om

of a liquid composed of miscible solvents A and B of refractive index n 1 5 and n 1 3 respectively The refractive index of prism is n 15 and that of the liquid is given by n CAA 1 CA ng where CA is the percentage of solvent A in the liquid C 90 80 a 70 60 50 0 Liquid inlet If 0 is the critical angle at prism liquid interface the plot which best represents the variation of the critical angle with the percentage of solvent is C 90 80 c 70 60 50 0 0 5 n 1 0 5 L 80 b 70 60 50 ICA C 90 C 90 80 d 70 60 50 1 CA Liquid Loutlet 0 5 0 5 1 CA ICA

Particles of masses 2M m and M are respectively at points A B and C with AB 1 BC m is much much smaller than M and at time t 0 they are all at rest At subsequent times before any collision 2 takes place 2 3 rect Answer 3 m will remain at rest m will move towards M m will move towards 2M m will have oscillatory motion

7 A mass M is split into two parts m and M m which are separated by a certain distance The ratio m M which maximizes the gravitational force between the parts is a 1 4 b 1 3 d 1 1 c 1 2 C

Ganymede Jupiter Figure 5 Figure 5 shows one of the four Galilean moons Ganymede orbiting the planet Jupiter and has an orbital period of 172 hours The distance between Ganymede and Jupiter is approximately 1 07 x 10 m The mass of Ganymede is 1 48 x 10 kg and the mass of Jupiter is 1 90 x 10 kg 29 What is the orbital and angular velocity of Ganymede around Jupiter a 1 01 x 10 rad s 1 09 x 10 m s b 2 11 x 10 rad s 4 37 x 10 m s c 1 76 x 10 rad s 2 56 x 10 m s

32 A body is released from a point distance r from the centre of earth If R is the radius of the earth and r R then the velocity of the body at the time of striking the earth will be a gR c 2gRr Vr R b 2gR d 2gR r R r

Consider the following image of the moon Observe that the line separating the illuminated side and the shadowed side is an ellipse arc Let the length of the semi major axis of this ellipse be a the semi minor axis be b and the angle between the sun and the moon as seen from earth is What is the correct expression for the sun moon earth angle B in terms of a and b a w b qr oww Dzi w a356 ominw wquat Aarde d w moni a b c d e B cos 1 B cos 1 B sin 1 10 PIC GIR B B cos 1 sin a b la b

57 What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R a c GmM 3R 2GmM 3R b d 5GmM 6R GmM 2R 2013

SA 4 Two trucks with equal mass are attracted to each other with a gravitational force of 6 7x10 N The trucks are separated by a distance of 0 4 km What is the mass of one of the trucks G 6 673x10 N m kg

identical bricks each of length L are placed as shown in figure The centre of mass of the system is from O at a distance 11L L L 2 b L 4 13L

P where M mass of earth m mass of the particle and rits distance from the centre of the earth If we now calculate the work done in lifting a particle from r r to r r r r along a vertical path we get instead of Eq 8 20 W S GMm r dr

2 Figure shows a cubical box that has been constructed from uniform metal plate of negligible thickness The box is open at the top and has edge length 40 cm The z co ordinate of the centre of mass of the box in cm is L AZ O

A uniform solid 1000 0 kg sphere 1 has a radius of 5 00 m Find the gravitational force this sphere exerts on a 2 00 kg point mass placed at a distance of 2 50 m from the centre of the sphere O 2 67 X 10 9 N O 2 47 X 10 9 N O 2 07 X 10 9 N O 2 27 X 10 9 N

An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the earth Suddenly due to internal explosion the satellite breaks into two parts of equal masses One part of the satellite stops just after the explosion and then falls to the surface of the earth Given acceleration due to gravity on the surface of earth is g D R A The increase in the mechanical energy of the system satellite earth due to explosion will be mgR 4 B Increase in the mechanical energy of the system satellite earth due to explosion will be 3mgR 4 C One part of the satellite which was moving after explosion is going to escape the gravitation field of earth D One part of the satellite which was stationary after explosion is going to collide on earth surface with a velocity which is double of its orbital velocity in original circular orbital

A satellite is to be launched in a circular orbit of radius ro around a planet of radius R For this two stage rocket is to be used First stage rocket is used to lift the satellite vertically up to the desired height ro measured from the center C of the planet after launching it from a launch point P Distance of launch point P from centre of the planet is rL Launch point P lies inside the tunnel as shown in the figure Second stage rocket is used to impart it a tangential velocity so as to put it in a circular orbit Let E and E2 are the energies delivered by the first and second stage of the rocket Assume that the mass of the rocket is negligible with respect to the mass of the planet and atmospheric resistance to be zero List I gives 4 values of ro and rL and List Il gives magnitude of some quantity ions 1 II III IV List I 10 R L To L R To 4R L R 2 3R 2 L R To 4R 10 00 2 correct match for P I S II T III U IV P I P II Q III T IV S I S II T III R IV P List II R 7 2 1 Q 1 11 6 S 2 T 6 U 8 C R E E for the values of ro and rL given in List I is ro

Two bodies of masses 10kg and 100 kg are separated by a distance 2m The gravitational potential at the mid point of the line joining the two bodies is a 7 3x10 7 J Kg b 7 3x10 J kg c 7 3x10 8J Kg d 7 3x10 6J kg

An isoscles right angle tunel ABO is made inside the earth from suraceof earth to its centre as shown in the fgure The distance between the points A and B and that between the points B and O is R 2 where R is the radius of earth The surface of tunnel is assumed to be frictioniess A smallparticle of mass m s released from point A The collisin between the particde and the tunnel is assumed to be perfetly elastic Take mas of earth M radius of earth R 6400 km and g 10 m s then find i The time taken by the particle to move in the tunnel from A to O and also find ii work done by gravitation field of earth on the particle to reach from B to 0 A B

The magnitude of the suns gravitational filed experienced by Earth is a Same over the year b Decreases in the month of July c Decreases in the month of July and increases in the month of January d Increase during day time and decreases during night time

0 The value of acceleration due to gravity is maximum at A the equator of the Earth B the centre of the Earth C the pole of the Earth D slightly above the surface of the est la

An artificial satellite of the earth releases a package If air resistance is neglected the point where the package will hit with respect to the position of artificial satelite at the time of release will be 1 ahead 2 exactly below 3 behind

An isosceles right angle tunnel ABO is made inside the earth from surface of earth to its centre as shown in the higure The R distance between the points A and B and that between the points B and O is where R is the radius of earth The surface 2 tunnel is assumed to be frictionless A small particle of mass mo is released from point A The collision between the particle 6400 km and and the tunnel is assumed to be perfectly inelastic Take mass of earth is M Radius of earth R g 10 m s Now answer the following question A Or R B 2 The time taken by the particle to move in the tunnel from A to O 1600 S 800T S 400 S

kept equal circle of radius R as shown Now if any one of them is taken very slowly from this position to infinity by performing W amount of work For next time th amount of work performed W upon another point mass which is diametricall opposite to previous one is again taken from its position to infinity very slowl are related as A W W B W W Gm 2R Gm 2R Gm 2R C W W 7 6 8 5 R 2 3