Gravitation Questions and Answers

A small particle of mass m is attached at one end of a light string of length and other end is connected to the ceiling of a satellite revolving around earth in circular orbit The satellite is at height h 2R above earth surface The period of oscillation of mass will be Re radius of earth 2 3R g 6 Zero Infinity

Two bodies A and B have masses M and m respectively where M m and they are at a distance d apart Equal force is applied to each of them so that they approach each other The position where they hit each other is a nearer to B b nearer to A c d 8 Two part 21 3j of mass

4 Find the altitude at which the acceleration due to gravity is 25 of that at the surface of the earth Radius of the earth R 6400 km

018 part 1 of 3 10 0 points Given G 6 67259 10 1 Nm kg After a supernova explosion a star may un dergo a gravitational collapse to an extremely dense state known as a neutron star in which all the electrons and protons are squeezed to gether to form neutrons A neutron star hav ing a mass of 1 9 x 1030 kg about equal to that of the Sun would have a radius of about 5 18 km Find the free fall acceleration at its surface Answer in units of m s 019 part 2 of 3 10 0 points Find the weight of a 40 3 kg person at its surface Answer in units of N 020 part 3 of 3 10 0 points Find the energy required to remove a particle of mass 1 35 x 10 27 kg from its surface to infinity

Three identical bodies each mass M are placed at vertices of an equilateral triangle of arm L keeping the triangle as such by which angular speed the bodies should be rotated in their gravitational fields so that the triangle moves along circumference of circular orbit 2 1 3GM VL GM L 3 GM V 31 4 3 GM L

Given G 6 67259 x 10 1 Nm kg After a supernova explosion a star may un dergo a gravitational collapse to an extremely dense state known as a neutron star in which all the electrons and protons are squeezed to gether to form neutrons A neutron star hav ing a mass of 1 9 1030 kg about equal to that of the Sun would have a radius of about 5 18 km Find the free fall acceleration at its surface Answer in units of m s 019 part 2 of 3 10 0 points Find the weight of a 40 3 kg person at its surface Answer in units of N 020 part 3 of 3 10 0 points Find the energy required to remove a particle of mass 1 35 x 10 27 kg from its surface to infinity Anemor in

2 0 m s The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant The force of air resistance on the balloon acts opposite to the direction of velocity and is proportional to it The balloon carries a mass M and is found to fall down near the earth s surface with a constant velocity v How much mass should be removed from the balloon so that it may rise with a constant velocity v

B A ball is projected upwards from a height h above the surface of the earth with velocity v The time at which the ball strikes the ground is 1 3 2h g Vg 1 1 2gh v 2 2v 2h g Vg 4 None of these mc0245

The gravitational force between two objects is proportional to 1 R and not as 1 R2 where R is separation between them then a particle in circular orbit under such a force would have its orbital speed v proportional to 1 1 R 3 R1 2 RO 4

b Given that an earth satellite near the earth s surface takes about 90 minutes per revolution and that a moon satellite takes also about 90 minutes per revolution Compare the densities of the earth and the moon Show that Newton s second law of motion remains invariant

A uniform bar AB of mass M and length L has a particle of mass m held at a distance a from end A as shown The gravitational force exerted by the bar on mass m in given by m Gm M a Gm M a L a Gm M LAL a M L B

A saturn year is 29 5 times the earth year How far is the saturn from the sun if the earth is 1 5 108 km away from the sun a 1 2 10 km c 1 4 x 10 km b 1 3 x 10 km d 1 5 10 km

Two space stations A and B are orbiting the earth with speed u in the same orbit of radius R Station B is a distance s ahead of station A Two astronauts from station A have to join the station B For this purpose they leave station A in a spaceship and move radially to a slightly lower orbit and stay in that orbit and when the station B comes closest to them they immediately move radially to join the station B If time spend in the lower orbit is At find separation between the orbits 2 sp 3v

diame as a solid sphere of uniform density Show that if a harmonic motion Calculate the time period of this particle is released in this tunnel it will execute a simple motion Solution

Calculate the ratio of the angular momentum of th earth about its axis due to its spinning motion to the about the sun due to its orbital motion Radius of th earth 6400 km and radius of the orbit of the eart

31 The distance of Neptune and Saturn from sun are nearly 1013 and 1012 meters respectively Assuming that they move in circular orbits their periodic times will be in the ratio 1 10 2 100 4 1 10 191 10

6 4 6N Iwo bodies A and B having masses m and 2m respectively are kept at a distance d apart A small particle is to be placed so that the net gravitational force on it due to the bodies A and B is zero Its distance from the mass A should be d 2 X X 1 2 1 x X 3 x d 1 3 4 x X d 1 4 d 1 6

ith it application of concepts How can you differentiate between a contact force and a force at a distance AS Find the net forces from the following diagrams uscul 5 alios 88 SN A man stand still on a levet floor What forces act on him Draw a free body diagram FBD to show all forces acting on him AS 4 The surface area of an object is 20 m and a force of 10 N is applied on it then what is the pressure AS How do you appreciate the role of friction in facilitating our various activities AS 6 Identify and draw all forces acting on the body shown in the diagram AS Higher Order Thinking Questions ON 1 If you push a heavy box which is at rest you must exert some force to start its motion However once the box is sliding you apply a lesser force to maintain that motion Why AS 2 How do you increase the pressure by keeping AS b force unchanged Multiple Choice Questions I Hoisting a flag is related to a push b pull a area unchanged 3 Imagine that friction disappeared from the earth What will happen Explain AS c Push and pull both d pressure 2 A person is pulling water from well Which type of force it is a Muscular force b Magnetic force c Friction force d Electrostatic force The force that a solid surface exerts on any object in the normal direction is called bi ICI

If a rocket is fired with a speed v 2 gR near the earth s surface and coasts upwards its speed in the intersteller space is 1 4 gR 3 gR 2 4 2gR 4gR

Five bodies of mass m m m m mo placed at corners of a pentagon as shown in figure The net ravitational force on body of mass m placed at centre is 2 m Gmm m a a m a m a a m mo Gm m m 4 Gm m m

Consider two solid uniform spherical objects of the same density p One has a radius R and the other 2R They are in outer space where the gravitational force due to other objects is negligible If they are at rest with their surfaces touching what is the force between the objects due to their gravitational attraction 158 1 G R p 81 168 3 G R p 81 2 4 128 81 148 81 G R p G R4p

1 If g be the acceleration due to gravity on the earth s surface the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is A mg R C 2 mg R B 2 mg R D mg R 4 I I T 1983

Gravitational force between two masses at a distance d apart is 6N If these masses are taken to moon and kept at same separation then the force between them will become 1 1 N 2 N 6 3 36 N 4 6 N

Newton s law of gravitation 1 is not applicable out side the solar system 2 is used to govern the motion of satellites only 3 control the rotational motion of satellites and planets 4 control the rotational motion of electrons in atoms

4 Mars has a diameter of approximately 0 5 of that of earth and mass of 0 1 of that of earth The surface gravitational field strength on mars as compared to that on earth is a factor of 1 0 1 2 0 2 3 2 0 4 0 4

A satellite of mass 2000 kg is revolving in elliptical path around earth If mean altitude at perigee and apogee are 1600 km and 5600 km respectively then the energy required to send the satellite in this orbit will be Radius of earth is 6400 km 1 7 2 x 10 0 J 2 7 8 x 1010 J 3 8 5 x 1010 J 4 5 6 x 1010 J

13 Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non rotating uniform sphere of density p The gravitational force on a particle of mass m dropped into the tunnel when it reaches a distance r from the centre of earth is 3 1 2 mGp r 3 4 m r 2 4 4 4T mGp r 3 4 m Gr

Two particles of equal mass go around a circle of radius r under the action of their mutual gravitational attraction The speed of each particle is 1 v 3 v 1 2R 1 21 1 GM GM 2R 2 v 4 v GM 2R 4GM R

Mass of the earth is 81 times that of the moon If the distance between their centers is d then the point on the line joining their centers at which the gravitational field due to them is zero is d 1 from the center of moon 10 d 2 3 10 9d 10 d from the center of earth from the center of moon from each other

59 A satellite is revolving round the earth with orbital speed v If it stops suddenly the speed with which it will strike the surface of earth would be v escape velocity of a particle on earth s surface hot b 2v c v v d v 2v 2 e a 2

If the apparent weight of the bodies at the equator is to be zer then the earth should rotate angular velocity rad sec B rad sec C 2R rad sec D TOE rad sec Mall Jhalawar Road Kota Raj 3

5 Consider two point masses m and 2m at a distance of 3 m in a gravity free space Find the maximum possible velocity Vo which can be given to 2m so that 2m and m revolve in a closed orbit due to their mutual gravitational force of attraction 2 Gm 1 4Gm V3 4 3 Gm

2 11 When the sun is directly overhead the surface of the earth receives 14 x 10 W m2 of sunlight Assume that the light is monochromatic with average wavelength 500 nm and that no light is absorbed in between the sun and the earth s surface The distance between the sun and the earth is 1 5x 10 m a Calculate the number of photons falling per second on each square metre of earth s surface directly below the sun b How many photons are there in each cubic metre near the earth s surface at any instant c How many photons does the sun emit per second

35 The ratio of radii of earth to another planet is 2 3 and the ratio of their mean densities is 4 5 If an astronaut can jump to a maximum height of 1 5 m on the earth with the same effort the maximum height he can jump on the planet is a 1 m b 0 8 m c 0 5 m d 1 25 m

182 Pre Medical Physics Illustration 14 Draw a rough sketch of the variation in weight of a spacecraft which moves from earth to moon Solution M K K F r m Fm Mm ml bo b

12 Energy required to move a body of mass m from orbit of radii 2R to 3R is 1139 2 1 GMm 2R GMm GMm 3R GMm

7Neglect the effect of rotation of the earth Suppose the earth suddenly stops attracting objects placed near its surface A person standing on the surface of the earth will a fly up b slip along the surface c fly along a tangent to the earth s surface d remain standing

16 A satellite revolves around a planet in circular orbit of radius R much larger than the radius of the planet a time period of revolution T If the satellite is stopped and then released in its orbit Assume that the sate experiences gravitational force due to the planet only A It will fall on the planet B The time of fall of the satellite is nearly T 8 C The time of fall of the satellite on the planet is nearly ZT 8 D It cannot fall on the planet so time of fall of the satellite is

Two bodies of masses m and m2 are connected by a long inextensible cord of length L The combination is allowed to fall freely towards the earth mass me the direction of the cord being always radial as shown in the figure Find a the tension in the cord and b the accelerations of m and m2 Does the cord ever become slack ignore the gravitational interaction between m and m A body is thrown up radially O me 1 U Earth m m

14 Two bodies of different masses are dropped simultaneously from the top of a tower If air resistance is proportional to the mass of the body 1 the heavier body reaches the ground earlier 2 the lighter body reaches the ground earlier 3 both reach the ground simultaneously 4 cannot be decided

bjec A body weighs 700 g on the surface of the earth How much will it weigh on the surface of a planet 1 and radius is half that of the Earth whose mass is A 200 gwt B 400 gwt C 50 gwt D 300 gwt

96 A jet airplane travelling at the speed of 500 km h ejects its products of combustion at the speed of 1500 km h relative to the jet plane The speed of the products of combustion with respect to an observer on the ground is a 500 km h c 1500 km h 1 b 1000 km h 1 d 2000 km h 1

terk in 2 DOUR ZUS A person moves 30 m along north direction then moves 40 m along east direction and ally 20 m along south direction Find distance displacement covered Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in figure What is the magnitude of the displacement for each For which girl this is equal to the actual length of path skate

For the 2 short answer ranking questions you will use the information from the pictures to answer the questions You must show your work 2 points rank the letters correctly 1 point and carefully explain your reasoning and or the equation you used for your answers 1 point The figures below all represent different size balls thrown upwards at different speeds A D Ball A mass 450 g speed 35 m s Ball D mass 650 g speed 40 m s B E Ball B mass 650 g speed 25 m s Ball E mass 250 g speed 35 m s C F Ball C mass 550 g speed 30 m s Ball F mass 400 g speed 45 m s 1 List the balls in order from lowest to highest below based on their maximum heights 2 List the balls in order from lowest to highest below based on the gravitational force exerted after being thrown

5 If the gravitational force were to vary inversely as mth power of the distance then the time period of a planet in circular orbit of radius r around the Sun will be proportional to 1 r 3m 2 3 m 1 2 2 r3m 2 4 r m 1 2

A planet in an orbit sweeps out an angle of 160 from March May when it is at an average of 140 million km from sun If the planet sweeps out an angle of 10 from October December then the average distance from sun is

9 Four moles of a gas enclosed in a container is heated at constant pressure The temperature of the gas increases by 3 C The work done by the gas is R gas constant 1 4 R 10 2 6 R 4 12 R

of e equal to the radius of the earth above the tunnel dug through the earth as shown in the figure Hence the correct statement is som 2 R seghe is forisiq YOU edi bauons OR TRIC Revivido aws e talge erit bris qille 1 Particle will oscillate through the earth to a height h R on both sides ottan 1 2 Motion of the particle is periodic 3 Motion of the particle is simple harmonic 4 Both 1 2 6 The particles A and B of mass meach are separated 3GM 2R 3 25 If potential en surface of ear energy at heig is radius of e GMm 1 R h GMml 3 R R 26 A particle V 4g F 3 particle

Assertion The weighing machine measures the weight of a body means the absence of Reason Weightlessness weight 1 A 2 B 3 C 4 D

Panton 2 Two plane mirrors are placed back to back They are then opened out slowly to form a wedge their reflecting surfaces lying on the outside A beam of parallel light becomes incident on the edge of the wedge The two beams reflected from its faces are found to make an angle of 100 with each other Determine the angle between the mirrors Ans 50