Gravitation Questions and Answers

Suppose a tunnel is made in earth which passes through its centre If an object is dropped from R height from earth surface above the tunnel If its 2 R speed at depth from earth surface in tunnel is 2 NGM 12R mass of earth and R is radius of earth then value of N is Given M is

4 Zero A point mass m is placed at a distance R from the surface of a solid sphere of mass m and radius R The gravitational potential energy of this system of point mass and sphere is 1 2 Gm 28 2 2 Gm R

three parallel straight wires placed perpendicular to plane of paper carrying same current I along the 03 same direction is BO 2 a Hoi 2nd d AO 90 shown in figure Magnitude of force per unit length on the middle wire B is given by NEET 2017 b 2 01 c nd d v oi 0 nd d 2 Hoia 2 nd

5 An apple of mass 0 25 kg falls from a tree What is the acceleration of the apple towards the earth Also calculate the acceleration of the earth towards the apple Mass of the earth 5 983 x 1024 kg Radius of the earth 6 378 106 m and G 6 67 x 10 11 Nm kg 2

BEGINNER S BOX 9 If two forces act in opposite direction then their resultant is 10N and if they act mutually perpendicu their resultant is 50N Find the magnitudes of both the forces

Electric potential in an electric field is given as V K r K being constant if position vector r 21 33 6k then electric field will be 21 31 6k K 343 61 2j 3k K 343 1 3 21 3j 6k K 243 31 2j 6k K 243 2 4

Example 18 In a double slit pattern 6000 the first order and tenth order maxima fall at 12 50 mm and 14 75 mm from a particular reference point If is changed to 5500 A find the position of zero order and tenth order fringes other arrangements remaining the same fris

A planet is moving in an elliptical orbit T U E and L are its kinetic energy potential energy total energy and magnitude of angular momentum respectively then which of the following statement is true 1 T is conserved 2 Vis always positive 3 is always negative OMO L is conserved but the direction of vector L 11

direction An artificial satellite is moving in a circular orbit of radius 42250 km Calculate its speed if it takes 24 hours to revolve around the earth 845

10 The distance between the centres of the earth and the moon is 60 times the radius of the earth Calculate the centripetal acceleration of the moon Acceleration due to gravity on the earth s surface 10 m s Ans 1 360 m s 2 2 1 The mean distance of earth from sun is 1 496 108 km and its sidereal revolution period is 365 3 days The sidereal revolution periods of the planets Venus and Mars are 224 7 days and 687 0 days respectively Estimate the mean distances of these planets from the Ans 1 082 108 km 2 279 x 108 km sun 0

At what height above earth s surface value of g is same as in a mine 100 km deep 292691096 begge 24 01 Corp Reg Office CG Tower A 46 52 IPIA Near City Mall Jhalawar Road An

3 At what height above the earth s surface would the acceleration due to gravity be i half ii one fourth of its value at the earth s surface Radius of earth 6400 km Ans i 2650 km ii 6400 km

3 The distance of the moon from the earth is about 60 times the radius of the earth What will be diameter of the earth approximately in degrees as seen from the moon a 1 b 2 c 4 d 6

5 A body is revoluing around sun with closest of 8 x 10 0 m and farthest distance of distance 1 x 10 2 m Time period of the body will be The mass of sun is 2 x 1030 kg 1 6 85 year 2 3 6 year 3 10 8 year 4 12 year

There is an isolated planet having mass 2M and radius 2R where M and R are the mass and radius of the earth A simple pendulum having mass m and length 2R is made to small oscillations on the planet Find the time period of SHM of pendulum in second take 3 00 g 10 m s 2 1 41

9 A model rocket fired from the ground ascends with a constant upward acceleration A small bolt is dropped from the rocket 1 0 s after the firing and fuel of the rocket is finished 4 0 s after the bolt is dropped Air time of the bolt is 2 0 s Acceleration of free fall is 10 m s2 Which of the following statements is are correct a Acceleration of the rocket while ascending on its fuel is 8 0 m s b Fuel of the rocket was finished at a height 100 m above the ground c Maximum speed of the rocket during its upward flight is 40 m s d Total air time of the rocket is 15 s

R d At a point A on the earth s surface the angle of dip 8 25 At a point B on the earth s surface the angle of dip 8 25 We can interpret that NEET 2019 1 A and B are both located in the southern hemisphere 2 A and B are both located in the northern hemisphere 3 A is located in the sourthern hemisphere and B is located in the northern hemisphere 4 A is located in the northern hemisphere and B is located in the southern hemisphere NEET 2019 and particles with same momenta enters perpendicular to a constant magnetic field B The

A small particle of mass mis 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 2Re above earth surface The period of oscillation of mass will be Re radius of earth 2 6 3R g Zona

4 Average density of the earth a is a complex function of g b does not depend on g c is inversely proportional to g d is directly proportional to g

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm Find the work to be done against the gravitational force between them to take the particle far away from the sphere you may take G 6 67 10 11 Nm kg a 3 33 10 10 J c 6 67 10 10 J b 13 34 10 10 J d 6 67 10 9 I

Assertion Mass is a property of one object alone whereas weight results from the interaction of two objects Reason The weight of an object is proportional to its mass

1 Two projectiles one fired from the surface earth with speed 5 m s and the other fired from the surface of a planet with initial speed 3 m s with some angle of project trace identical trajectories Neglecting friction effect the value of acceleration due to gravity on the planet is 2 3 5 m s 08 4 8 5 m s2 183 1 5 9 m s STU 3 16 3 m s 8

The masses and radii of the earth and moon are M R and M R respectively Their centres are at distance d apart The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is 2G M M 1 4GM M d 2 4G M M d G M M d 9

A satellite is moving with a constant speed v in circular orbit around the earth An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth At the time of ejection the kinetic energy of the object is 3 mv 2 72 2 my

A particle of mass M is situated at centre of a spherical shell of same mass wit adius R The change in gravitational potential when mass is taken to surface of the shell is O O GM 2R GM 2R 3 GM 2 R Zero

The additional kinetic energy to be provided to a satellite of mass M revolving around a planet of mass Mo to transfer it from a circular orbit of radius R to adius R R R is GMOM R R 2 R R GMOM R R 4 R R GMM RZ R 2 R R B R

Ro The acceleration due to gravity at poles and at equator is go and ge respectively f earth were a sphere of radius Re and rotating about axis with angular speed We then gegp is given by R We Maik T01 Ro 90 90 min sec

Orbital velocity of a given artificial satellite moving in a circular orbit just above the earth s surface is Vo The value of orbital velocity for another satellite orbiting at height half of earth s radius will be given by 3 A Vo B C 3 VO Correct Answer 2 3 Vo

If at a small height h above the surface of earth acceleration due to gravity decreases by 0 2 then at depth h below the surface of earth the acceleration due to gravity will 1 Increase by 0 4 2 Increase by 0 1 3 Decrease by 0 4 4 Decrease by 0 1

What will be the acceleration due to gravity at a point which is at the distance R from 4 Earth s centre R is radius of earth go is acceleration due to gravity at surface of earth Question Type Single Correct Type 1 2 3 90 4 3go 4 90 2

Zero Marks 0 In all other cases A satellite with mass 2000 kg and angular momentum magnitude 2 10 2 kg m s moving in an elliptical orbit around a planet The rate at which area is being swept out by the satellite around the planet is equal to 10 m s find x y maturu u me TERMENIMA with the

If Gravitational field due to uniform thin hemispherical shell at point P is I then the magnitude of gravitational field at Q is Mass of hemisphere is M radius R P 2R 2R

Gravitational field at the centre of a semicircle formed by a thin wire AB of mass m and length as shown in the figure is Gm 2 along x axis Gm TL along y axis 2 Gm along xaxis 22 27Gm 12 along y axis A B B

Negative Marks 1 If wrong option is selected A planet moves in an elliptical path with the sun is at one of its foci Select the incorrect statement In QRP path work done by gravity is positive Linear velocity of rotation from Q to P via R decreases O In PSQ path work done by gravity is negative Gravitational potential energy increases in going from P to Q via S S S

Zero Marks 0 In all other cases A satellite is orbiting around the earth in an orbit in equatorial plane of radius 2Re where Re is the radius of earth If the area on earth this satellite covers for communication purpose in its complete revolution then find N

Negative Marks 1 In all other cases If the escape velocity for an object placed at the surface of the earth is ve then the escape velocity for the same object when projected from the point of a tunnel made along diameter of the earth from a depth of d 0 05R where R is the radius of the earth is Less than v by a factor of more than 5 Greater than v by a factor of more than 5 Less than ve by a factor of less than 5 Greater than v by a factor of less than 5

The acceleration due to gravity at the latitude 60 on the earth becomes zero if the angular velocity of rotation of earth equal to 2g R g 3R 5g R LOR

Two stars of masses 3 x 1031 kg each and at distance 2 x 10 1 m rotate in a plane about their common centre of mass O A meteorite passes through O moving perpendicular to the star s rotation plane In order to escape from the gravitational field of this double star the minimum speed that meteorite should have at O is Take Gravitational constant G 6 67 x 10 11 Nm kg 2 B 2 4 x 10 m s 1 4 x 105 m s 3 8 x 104 m s 2 8 105 m s

The escape velocity of a body from earth s surface is ve The escape velocity of the same body from a height equal to 7R from earth s surface will be Question Type Single Correct Type 1 2 Ve 2 Ve 2

9 Take the mean distance of the moon and the sun earth to be 0 4 106 km and 150 106 km respectively Their masses are 8 102 kg and 2 1030 kg respectively The radius of the earth is 6400 km Let AF be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and AF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth Then the number closest to is a 2 b 0 6 c 6 AF AF d 10

Consider two identical rings of mass M and radius R fixed on a horizontal axis in a gravity free space A particle of mass m is held at rest at the centre of 1st ring and projected along the axis towards 2nd ring The minimum speed of projection so that the particle reaches the centre of 2nd ring is M R M R m 14 2R 1st Ring 2nd Ring GM R 2GM V R 1 2 Correct Answer Your Answer 2GM R

speed in km s with which it hits the surface of the earth A bullet is fired vertically upwards with velocity v from the surface of a spherical planet When it reaches its maximum height its acceleration due to the planet s gravity is th of its value of the surface of the planet If the escape velocity from the planet is vev N then the value of N is ignore energy loss due to atmosphere 4

A satellite is launched and attains a velocity of 30400 km hr relative to the centre of the earth at a height of 320km from the earth s surface It has been guided into a path that is parallel to the earth s surface at burnout Choose the correct options a Satellite moves along an elliptical orbit b Longest distance from the earth s surface is 3550 km The period of revolution for the satellite is 2 09 brs

Sutingsm 30 Solve the following Certain stars are believed to be rotating at about 1 rot s If such a star has a diameter of 40 km what is the linear speed of a point on the equator of the star domoso 2 marks

Two rings each of radius a are coaxial and the distance between their centres is a The masses of the rings are M and M The work done in transporting a particle of a small mass m from centre C to C is Gm M M a

When energy of a satellite Earth system is non zero positive then satellite w Move around the earth in circular orbit Just escape out Move around the earth in elliptical orbit

A hydrogen balloon released on the moon would 1 climb up with an acceleration of 9 8 m s 3 neither climb nor fall 2 climb up with an acceleration of 9 8 x 6 m s 4 fall with an acceleration of 9 8 6 m s d R floot in water It is observed that A floats with half its volume immersed and B floats wi

A current of 10 A is passing through an aluminium wire of cross sectional area 4x10 m The density of the aluminium conductor is 2 7 g cc Considering aluminium gives 1 electron per atom for conduction then find the drift velocity of the electrons if molecular weight of aluminium is 27 g a 1 6 x 10 b 3 6 x 10 c 2 6 x 10 d 1 5x 10 m s m s m s m s

A smooth narrow tunnel is dug along the chord of earth The time period of vibration of a small ball dropped from one end of the tunnel is AVE f 1 60 minute 2 123 minute 2 84 6 minute 4 30 minute

175 A jet air plane travelling with a speed of 500 km h ejects its products of combustion with a speed of 1500 km h relative to the jet plane The speed of the latter with respect to an observer on the ground is 1 1500 km h 3 1000 km h 2 2000 km h 4 500 km h