Gravitation Questions and Answers

d m For a body to have its apparent weight at the equator to be zero the earth should rotate about its axis faster than its present value by a factor of Take g 10 m s and R 6 4 106 m a 7 b 17 c 27 d 37 the value of

The acceleration due to gravity at a hill station is less by 0 05 with respect to that at sea level What is the height of that hill station The radius of the earth 6400 km 1600 m

A body is thrown vertically upwards with a velocity v from the surface of the earth Show that the height h 2 R 28R 2i up to which the body will rise is given by h here R radius of the earth g acceleration due to gravity

10 A planet of mass Mis in an elliptical orbit around the sun with time period T The semi major axis and semi minor axis are equal to a and b respectively The angular momentum of the planet is 1 3 2M ab T M ab OT 2 Mab 4 2 abT

1 At what height from the surface of earth the gravitation potential and the value of g are 5 4 x 107 J kg and 6 0 m s 2 respectively Take the radius of earth as 6400 km NEET 2016 1 2000 km 3 1600 km 2 2600 km 4 1400 km

1 A satellite of mass 1500 kg is revolving around earth The radius of earth is 6400 km Minimum and maximum distance of satellite from surface of earth are 1200 km and 2400 km respectively The approximate time period of satellite is 1 2 h 2 11 5 h 3 19 2 h 4 4 07 h

Q17 The gravitational field in a region is given by E 31 41 N kg Find out the work done in joule in displacing a particle by 1 m along the line 4y 3x 9

A rocket starts vertically upward with speed vo Show that its speed v at height h is given by u u 2gh h 1 R where R is the radius of the earth llu upwards from the surface

What will be the value of the acceleration due to gravity g at a height 3200 km from the earth while its value at the earth is 9 8 m s Radius of the earth is 6400 km Ans 4 35 m s 2

An orbiting satellite will escape if A its speed is increased by 2 1 100 B its speed in the orbit is made 1 5 times of its initial value C its KE is doubled D it stops moving in the orbit C

A satellite is revolving 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 O 1 GM 2V R 3 GM 2V R A ZQPO 90 and V B ZQPO 127 and V C ZQPO 53 and V D ZQPO 127 and V 3 2GM R GM satellite will traverse an ellipse satellite will traverse an ellipse satellite will escape satellite will escape

If the earth stops rotating about its axis then what will be the change in the value of g at a place in the equator plane Assume that the earth is a sphere of radius 6 4 x 106 m

The average distance of the sun from the earth is 1 5 108 km and the average distance of the moon from the earth is 384000 km If the attraction of the sun on the earth is 180 times the attraction of the moon how many times is the mass of the sun greater than that of the moon 2 75 107

The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the earth surface of earth hradius of earth is ts benelg 1 3 h 1 1 2 1 R 2 ng 4 1 1 2h R S

A solid sphere of mass M and radius R has to be disintegrated into infinite point masses at infinite separation The work done for this process will be G universal gravitational constant 1 1 3 GM R 2GM 2 4 GM R A 3GM Fol ED

A cell of e m f e having an internal resistance r is connected to an external resistance R The potential difference V across the resistance R varies with R as shown in figure Then correct curve is V 1 A 3 C A B C D 2 B 4 D R

Suppose the acceleration due to gravity at the earth s surface is 10m s and at the surface of mars it is 4 0 m s A 60kg passenger goes from the earth to the mars in a spaceship moving with a constant velocity Neglect all other objects in the sky Which part of figure best represent the weight Net gravitational force of the passenger as a function of time Weight N 600 400 240 200 2 B B C Time 3 C 4 D

5 A spaceship orbits around a planet at a height of 20 km from its surface Assuming that only gravitational field of the planet acts on the spaceship what will be the number of complete revolutions made by the spaceship in 24 hours around the planet Take mass of planet 8 x 1022 kg radius of planet 2 106 m gravitational constant G 667x10 1 N m kg LIFE Main 2019 10 April Shift II

7 A person stands on a spring balance at the equator a By what fraction is the balance reading less than his true weight b If the speed of earth s rotation is increased by such an amount that the balance reading is half the true weight what will be the length of the day in this case Jooms

A satellite is revolving around earth with orbital speed vo If it stops suddenly find the speed with which it will strike the surface of earth v escape velocity I mis 1 5 0 2 Vo Im

Gravitational potential at the centre of a solid sphere is V Now radius of this sphere is made double its present value without changing its mass Then the potential on the surface of this new sphere will be V 1 2V 3 3V 2 4 N m

A space vehicle is in a circular orbit about the earth Mass of the vehicle is 3000 kg and radius of orbit is 2Re 12800 km It is desired to transfer the vehicle to a circular orbit of radius 4Re along an elliptical path as shown Velocity change required at A is 2Re 4Re

The electrical force like the bodies force decreases inversely as the square of the distance between charged

Problem 3 A meteoroid is heading directly to the Earth The speed of the meteroid is 2000 m sec when it is at a distance of 3 84 x 10 m from the Earth this is the distance between Earth and the Moon At what speed will this meteroid strike the surface of the Earth The mass of the Earth is 5 972 x 1024 kg and the radius of the Earth is 6 371 x 10 m You may ignore the loss in energy due to the drag from the Earth s atmosphere Answer 1 13 x 10 m sec 11 3 km sec

kg Mars has a mass of about 6 57 1023 and its moon Phobos has a mass of about 9 x 10 5 kg If the magnitude of the gravitational force between the two bodies is 4 95 x 10 5 N how far apart are Mars and Phobos The value of the universal gravitational constant is 6 673 10 N m kg2

Maun 1 989 x103 kg Raun 696 340 km Meath 5 972 x 10 4 kg REarth 6 371 km G 6 67x10 11 c 3 0 x 10 m s An asteroid has a mean radius of orbit around the center of the Sun of 4 83x10 11 m a What is its orbital period 2 b Determine its orbital speed 2 c Determine the speed that would be required for the asteroid to escape from the Sun s orbit at this radius

spacecraft Wh a mass of about 400 000 kilograms kg Brett thinks Earth would exert the same gravitational force on a less massive spacecraft as it does on the ISS Rachel thinks the gravitational force would be different because an object s weight on Earth depends on its mass and gravity Brett and Rachel investigate how gravitational forces in newtons N affect objects of different masses in kilograms using a simulation Select a mass from the menus for Objects 1 and 2 Then click Run to watch the simulation ext run at least three more trials with varying asses for both objects 47 LARAIB Which student is correct Explain which objects and observations in simulation support your answer Enter your answer in the box provi BI UT 1 2 5 HEE X54 I MTE 2

F Gm1m r2 1 ac 2 T T GM R 1 Vesc 2GM R Gm1m KE mv U E KE U Ecircular Gm m 1 2r T G 6 674 x 10 1 N m kg Problem 1 You are the science officer on a visit to a distant solar system Prior to landing on a planet you measure its radius to be 9 x 100 m and its rotation period to be 22 3 hours You have previously determined that the planet orbits 2 2 x 10 m from its star with a period of 402 days 3 473 x 107 sec Once on the surface you find that the free fall acceleration is 12 2 m sec a What is the mass of the planet Answer 1 5 x 1025 kg b What is the mass of the star Answer 5 2 x 1030 kg

Problem 7 Planets Beyond the Solar System On October 15 2001 a planet was discovered orbiting around the star HD 6888 Its orbital distance was measured to be 1 05 x 100 m from the center of the star and its orbital period was estimated at 6 3 days 5 44 x 10 sec What is the mass of HD 68 Express your answer in kilograms and in terms of our sun s mass M 1 99 x 10 kg Answer M 231x10 kg 1 16M

Problem 6 Two satellites are in circular orbits around a planet that has radius 9 x 10 m One satellite has mass 68 0 kg orbital radius 7 x 107 m and orbital speed 4800 m sec The second satellite has massi 84 0 kg and orbital radius 3 x 107 m What is the orbital speed of this second satellite Answer 7332 1 m sec

Problem 2 A exoplanet is orbiting its parent star The radius of the orbit of the planet around the sta is 7 9 x 10 m and the orbital period of the planet around the star is 4 2 days 3 63 x 105 sec What is t mass of the star Express your answer in kilograms and in terms of our sun s mass Msun 1 99 x 1030 kg

F R 7 2 Gm1m G 6 674 x 10 N m kg KE mv U 7 roblem 1 Let s assume the Earth and Jupiter orbit the Sun in circular orbits The distance between the arth and the Sun is TE 1 5 x 10 1 m and the orbital period of the Earth around the Sun is TE 1 year he distance between Jupiter and the Sun is rj 7 8 x 10 1 m Calculate TJ the orbital period of Jupiter round the Sun in years 1 year 3 154 x 107 sec ac T 9 E KE U Ecircular Vesc R Gm m 2r

A Type la supernova has an effective temperature of 7000 K and the speed of the 5000 km s What is its abolute magnitude if it is 62 days old Select one a 18 9 O b 18 6 c 18 0 O d 18 3 e 19 2 date distance

Geostationary satellites are placed into orbit so that their period of rotation exactly matches Earth s rotation They take 24 h to make one rotation These satellites are permanently fixed above one point on the equator of Earth Calculate the height of the satellite above Earth s surface

2 A Determine the magnitude and direction of the gravitational field strength at a point in space 7 4 x 107 m from the center of Earth

4 Determine the mass of Earth using the magnitude of the gravitational field strength at the surface of the Earth g 9 8 m s the distance r between Earth s surface and its centre 6 38 x 106 m

3 Eris is the ninth most massive body orbiting the Sun It is more massive than Pluto and three times farther away from the Sun Eris is estimated to have a radius of approximately 1200 km Explore the force of gravity on the surface of Eris by solving the following three parts a Suppose that an astronaut stands on Eris and drops a rock from a height of 0 30 m The rock takes 0 87 s to reach the surface Calculate the value of g on Eris b Calculate the mass of Eris c Suppose that an astronaut stands on Eris and drops a rock from a height of 2 50 m calculate how long it would take the rock to reach the surface

7 A 0 0015 C particle charge feels a downward electrical force of 1 0 x 10 N at Earth s surface a What is the strength of the electric field at Earth s surface b How many excess electrons does this represent

6 What does it mean if an object is in free fall List an example

In the parallel Universe X the force of gravitational attraction varies directly with the two masses m1 and m2 and inversely with the cube of the distance between them It was measured that the force equals 100 N for the masses 2000 and 3000 kg separated by 5 meters Find the force for 4000 and 5000 kg separated by 10 meters

13 A hot air balloon is held down to keep it From accelerating upward

The following diagram represents Neptune Uranus and the Sun in a straight line Neptune is 1 63 x 10 2 meters from Uranus Sun Uranus Neptune 1 63x10 m Not drawn to scale Calculate the magnitude of the interplanetary force of attraction between Uranus and point Show all work including the uation and with

When a satellite is a distance R from the center of Earth the force due to gravity on the satellite is F What is the force due to gravity on the satellite when its distance from the center of Earth is 3R AF

a Find the magnitude of the gravitational force in N between a planet with mass 6 75 x 1024 kg and its moon with mass 2 35 x 1022 kg if the average distance between their centers is 2 30 x 108 1 99 10 20 N b What is the moon s acceleration in m s2 toward the planet Enter the magnitude 7 51 10 3 X m s c What is the planet s acceleration in m s2 toward the moon Enter the magnitude X m s 3 06 10 5

You are located inbetween 2 stars of different masses at a specific distance from each star Note each of the two stars will pull you in opposing directions Which pair of stellar masses and distances would result in you experiencing the lowest net force of gravity 10 solar mass star at 5 AU O b 8 solar mass star at 2 AU c 3 solar mass star at 3 AU O d 4 solar mass star at 6 AU a 12 solar mass star at 6 AU 32 solar mass star at 4 AU 7 solar mass star at 7 AU 6 solar mass star at 4 AU

You observe the light from a spectroscopic binary star system and determine the two stars have different masses However which of the following must they have in common as they orbit They will both Select one O A have the same temperature B produce the same spectral lines OC have the same orbital period OD be the same distance from the center of mass

5 Looking at the diagram below in which part of the orbit is the planet moving the fastest a A b B e none of the above C C d D A Sun D 6 If an orbiting satellite has a total energy of 1 4 x 10 2 J then the binding energy is a 1 4 x 10 2 J d 7 0 x 10 J b 1 4 x 10 2 J e not enough information c 2 8 x 10 2 J

a If gold were sold by weight would you rather buy it in Denver or in Death Valley O Denver O Death Valley O no difference b If it were sold by mass in which of the two locations would you prefer to buy it O Denver O Death Valley no difference Why

If I weigh 741 N on Earth at a place where g 9 80 m s 2 and 5320 N on the surface of another planet what is the acceleration due to gravity on that planet O 61 2 m s 51 4 m s2 70 4 m s2 81 0 m s

A stone is held at a height h above the ground A second stone with four times the mass of the first one is held at the same height The gravitational potential energy of the second stone compared to that of the first stone is Oone fourth as much O twice as much O one half as much O four times as much O the same