Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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
Physics
Gravitation
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