Gravitation Questions and Answers

Consider a planet of mass M and radius R as shown in the figure A particle is projected from the surface of the planet at an angle 8 from radial direction and with velocity equal to the orbital velocity of circular orbit at that point then choose the CORRECT statement s M R P Vo

Section A PHYSICS Raghav observed that dry leaves are falling on earth He understood the reason soon He though that those leaves attract earth 1 Which force exerts in between leaves and earth 2 Can leaves also attract earth Explain mathematically

Q 1 How much faster would a person be moving if they stood on top of a 23 7 m high building compared to the ground Take the period to be one day and the radius of the earth to be 6400 km 15 2 m s 0 00172 m s 0 465 m s 0737 m

Determine the kinetic energy a 5000 kg spacecraft must have in order to escape the Earth s gravitational field Mass of the earth 6 0 x 1024 kg radius of the earth 6 4 x 106 m G 6 67 10 11 N m kg a 3 14 x 10 1 b 3 04 x 10 J c 3 34 x 10 d 3 53 x 10 11

rod and a solid sphere are placed as shown in diagram Leng of rod is 4L and radius of sphere is L Mass of rod and sphere is m each centre of sphere lies on perpendicular bisector of rod then net force sphere due to rod will be Gm A 2 2 C Gm 2 4L 4L X m 2L of UK 2L Solid sphere B D LO m Gm 4L 2 Gm 2L 2

3 Weight of a body of mass m decreases by 1 when it is raised to height h above the earth s surface If the body is taken to a depth h in a mine then in its weight will 1 decrease by 0 5 om 3 increase by 0 5 2 decrease by 2 4 increase by 1

Gravitational field of a uniform solid sphere of mass m and radius R is given as where r is distance from centre of sphere Gmr 9 0 r R R3 Gm g reR r2 Gravitational field at height h above solid sphere s surface is equal to gravitational field at depth h below solid sphere s surface Then O h 0 42 R h 0 62 R h 0 33 R h 0 25 R

13 The two ends of a uniform thin rod of length 2 R and of mass 2 2 kg can move without friction along a vertical circular path of radius R The rod is released from the vertical position ab b d Find the force in N exerted by an end of the rod on the path when the rod passes the horizontal position cd

This section contains 1 Matrix Match type question which has 2 Columns Column I and Column II Colum four entries A B C and D Column II has four entries P Q R and S Match the entries in Colum with the entries in Column II Each entry in Column I may match with one or more entries in Column II The line joining the planet to the sun sweeps out area A B and C in time t 2 and to respectively as shown Match the columns Sun B Column II Column I A A B C P 1 1 B A B C Q 1 13 C B C A R ts D A B C S

A Law of gravitation gives the gravitational force between two bodies having any masses R When the distance between two objects is increased the force of attraction between them will decrease Only One Correct Answer A B Both A and R are true and R is the correct explanation of A Both A and R are true but R is not the correct explanation of A

1 Two planets A and B are revolving around the Sun have time period in the ratio of 27 2 2 then the ratio of their radius of revolution is Only One Correct Answer A B 2 9 9 2 C 3 4 Review D 4 3 LOB OG A AC L

16 A solid sphere has mass M uniformly distributed over its volume and a is radius of sphere What is the gravitational potential at the centre of the sphere x4 6 3 1 3 GM a 3 GM 2 4 3 GM 2 a GM

Suppose there are two planets X and Y Orbit of planet X lies between the orbits of Mars and Earth while orbit of planet Y lies between the orbits of Uranus and Neptune If both planets X and Y are moving in the orbit around the Sun with the same seed then A period of revolution of X is greater than that of planet Y B period of revolution of X is smaller than that of planet Y C period of revolution of X is equal to that of plane Y D none of these

Gravitational force between two point masses m and M separated by a distance r is F Now if the distance between them is halved the force between them becomes Only One Correct Answer A 4F C

The line joining the planet to the sun sweeps out area A B and C in time t and t3 respectively as shown below M the columns C Sun A B Column I A A B C P t 1 B A B C Q 12 13 C B C A R t 13 D A B C S t 13 Column II

Q 2 Attempt the following part a Define conservative force A planet of the so lar system has an elliptical orbit with a 5 8 10 km and e 0 20 Calculate the total mechanical en ergy and the aphelion and perihelion distances It is given that the mass of the planet is 3 3 x 1023 kg the mass of the Sun is 2 0 1030 kg and G 6 67 x 10 Nm kg2

tional Consider the force of attraction between you 35 kg and the earth The mass of the earth is about 6 x 1024 kg and its radius is about 6 400 km i e 6 4 106 m The distance between you and the centre of the earth is very nearly equal to the radius of the earth unless you are travelling in a spaceship or walking on the moon Thus the force of attraction on you by the earth is 24 1 OF 1

At the center of a non uniform ring of radius R made up of two uniform halves of mass 2M and M G Newton s gravitational constant A field and potential both are zero 3GM B field is zero but potential is C field is zero but potential is 2GM D magnitude of field is R GM R and potential is 3GM

The figure shows an infinitely long thin wire of uniform linearly mass density and two points P and Q Then 7 a P The gravitational field at P is 2G The gravitational field at Q is 2G a The gravitational potential difference between P and Q Vp Vo is 2G In2 The gravitational potential difference between Q and P Vo Vp is 2G In2

A projectile is field vertically upwards from the surface of earth with velocity KV where V is escape velocity and K 1 If R is the radius of the earth the maximum height to which it will rise measured from the centre of the earth will be neglect air resistance 1 2 1 K R 3 R 1 K 2 4 R 1 K R

A satellite orbits around the earth in a circular orbit with speed u and orbital radius r If it loses some energy then 1 u decreases and r increases 2 both u and r decrease 3 u increases and r decreases 4 both u and r increase

dA dt A planet revolves about the sun in elliptical orbit The arial velocity of the planet is 4 0 x 10 m s The least distance between planet and the sun is 2 10 2 m Then the maximum speed of the planet in km s is A 10 B 20 C 40 D None of these

Gravitation Calculate the gravitational potential energy of a 7 7 kg mass a on the surface the Earth and b at an altitude of 350 km c Take the difference between the results for parts a and b and compare with mgh where h 350 km

Determine the vibrational contribution to Cy for CO2 where 2349 cm 667 cm doubly degenerate and 3 1333 cm at T 210 K Express your answer in joules per mole kelvin CV Vib In AXO COO I J mol K 1

The centres of two stars of masses M and 16M of radii R and 2R are separated by a distance of 10R Draw a graph between gravitational potential V and the distance r from the centre of the smaller star along the line joining their centres for R r 8R M R 2R 16M KK 10R r

CD UPB 2016 09 umericals The average distance of the sun from a planet is 9 times in comparison to average distance of sun UPB 2014 Ans 27 years from earth Find the time tinit of rion of the planet

B D 7 Four tunnels are supposed to be bored through the earth between two places on a longitude as shown in the figure One of them with midpoint at A is straight whereas other three have bent at their midpoints B C and D Both the bent sections are coplanar A particle released from one end of the tunnels spends time intervals TA TB TC and TD respectively to reach the other end If the particle passes the bent smoothly without a change in speed there which of the following relations will these time intervals bear a TA TB Tc TD c TA TC TB TD b TA TC TB TD d TB TA Tc TD

If you wanted to determine the mass of a black hole in an X ray binary what would be easiest for you measure O a The radius of the event horizon O b The orbital distance period and mass of the companion star Oc The size of the companion star Od The orbital speed of the black hole around the centre of mass

A ring of uniform mass M and radius R is placed in Y Z plane with centre at the origin as shown A particle of mass m is released from point P x R as shown then choose the correct alternatives 0Q OQ R 2 MR OQ P R 52 During motion of the particle maximum possible magnitude of negative x coordinate will be equal to the OP Force acting on the particle at origin is zero Particle comes to rest at origin Particle will perform oscillatory motion

0 7 Dependence of intensity of gravitational field E of earth with distance r from centre of earth is correctly respresented by AIPMT 2014 Et 1 3 TLL R R 2 tw tw O 4 R R

16 A circuit contains an ammeter a battery of 30 and a resistance 40 8 ohm all connected in series If the ammeter has a coil of resistance 480 ohr and a shunt of 20 ohm the reading in th ammeter will be Re AIPMT 2015 1 1 A 3 0 25 A 2 0 5 A 4 2 A

At what distance from center of earth the gravitationa field strength is 25 of that at the earth s surface given that the radius of earth is R R 4 x 00 O 3R R2

A satellite close to the earth is in orbit above the equator with a period of rotation of 1 5 hours If it is above a point P on the equator at some time it will be above P again after time a 1 5 hours b 1 6 hours if it is rotating from west to east 24 c hours if it is rotating from west to east 17

Binary stars rotate under mutual gravitational force at separation 2 units where to is the angular velocity of each of the star about centre of mass of the system If difference between the mass of stars is 6 units Find the ratio of masses of bigger star to smaller star

SolveLancer Test An object of mass 50 kg dropped from a height of 20m on a planct The mass and radius are thrice that of earth Find the momenturn of the object the surface of the planet SolveLancer Test a 50 kg m s b 50 131 kg m s c 500 135 kg m s d 50v120 kg m s a b C

A satellite of mass mis rotating around earth in circular orbit of radius 3R What extra energy should be given to this satellite if it is to be shifted into a circular orbit of radius 4R M Earth mass GmM 24R Gm M 12R 3Gm M 8R

A Body falling into sun from a large distance A body starts from rest toward sun from a distance equal to the radius of earth s orbit around sun Find the time after which it will fall into sun Neglect the dimensions of sun in heliocentric reference frame

Consider two identical particles each of mass m held at a separation ro in free space One of them is given a velocity vo perpendicular to r and the other one is simultaneously released For what range of velocity vo will the masses be bound in orbital motion under their mutual gravitat ional forces a vo 2Gm V To v 2 Gm b vo 2Gm ro Gm d v 2

Spaceman Fred s spaceship which has negligible mass is in an elliptical orbit about Planet Bob The minimum distance between the spaceship and the planet is R the maximum distance between the spaceship and the planet is 2R At the point of maximum distance Spaceman Fred is traveling at speed v He then fires his thrusters so that he enters a circular orbit of radius 2R What is his new speed 1 3 2 vo 3 3 56 vo R 2R 2 5 vo 4 2 vo

153 The ratio of the energy required to raise a satellite upto a height h above the earth of radius R to that the kinetic energy of the satellite in that orbit is 1 R 2h 2 2h R 3 R h 4 h R

Two satellites are launched at a distance R from a planet of negligible radius Both satellites are launched in the tangential direction The first satellite launches correctly at a speed vo and enters a circular orbit The second 1 satellite however is launched at a speed V What is the minimum distance between the second satellite and 2 the planet over the course of its orbit Options 1 R 2 NH3 1 R

An accurate pendulum clock is mounted on ground floor of a high building How much time will it lose or gain in one day if it is transferred to top storey of a building which is h 200 m higher than the ground floor Radius of earth is 6 4 106m

An object of mass 50 kg dropped from a height of 20m on a planet The mass and radius are thrice that of earth Find the momentum of the object the surface of the planet SolveLancer Test a 50 kg m s

and r from centre of R and mass M are F and F respectively the find ratio of F and F Joy 1 3 4 F 12 2 2 F r 2 Fif R and r R F 12 1 if r R and r R F1 1 if R and r R F 12 F ifr R 4 F Gmbi 2 R3 if r R and r R R IF Pick F22 GMP If PILR 2 fi h F2 r2

Xor Three uniform spheres of mass M and radius R each are kept in such a way that each touches the other two Find the magnitude of gravitational force on any of sphere due to other two spheres 1 3 GM 4 R 2 4 3R 40 A planet of sun with tim minor axis angular mo 4mg 49 3 GM 2 R fnet 3F 3 GM 1 2M a T

nce r radius then SUN mass zelai M Min a circular orbit of radius r with angular speed w Another planet of mass 2m moves round the sun in circular orbit of radius 4r with angular speed 2 00 w Find the ratio of 1 4 3 8 2 6 mm mw h2 134 A satellite of m 4 4 100 8 C Gm h3 W1 GM an 38 8 com W 5 AN 39 A satellite speed v with whi V esc 1 3 Find the

ound the earth surface If of earth is g ting on the 2021 Sec d radius R Find the minimum energy required to launch a satellite of mass m from the surface of earth of mass Mand radius R in a circular orbit at altitude 2R Ju 1 Gmm 2 5 R R 2 5 GMM L 3 5R 46mm 4922 3 4 5GMm 6R P GMm 3R Gmm R K122 ammim 702 KE amm 3R 2 2GMm RE GMM Gmm amm 3R 6R R 3R 5 GMM NJ Gmm GMm 2R GR yamm 32 ml

ALLEN 9 Figure shows the variations of energy E with the 19 ff was from Efendi yfi orbit radius r of a satellite in a circular motion Choose the correct statement E 1 A shows the kinetic energy B shows the total energy and C the potential energy of the satellite 2 A and B are kinetic energy and potential energy respecitvely and C the total energy of the satellite 3 A and B are the potential energy and kinetic energy respectively and C the total energy of the satellite 4 C and A are the kinetic and potential energies and B the total energy of the satellite E 1 A Bann Caffe 2 AB fara sf qui fuf 3 AB feferat f 4 C i Afri fr

Six stars of equal mass m moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a Find net force on star due to other five stars O GM 5 a 4 GM 5 a O 4 2 1 GM 5 a 4 3 O GM 5 3

A near earth orbit satellite of earth experiences very small air resistance It s period of revolution decreases by 1 08 sec day 160 3 It s radius decreases by It s radius decreases by 160 3 m in 1 day m in 1 revolution It s angular momentum decreases It s mechanical energy increases