Gravitation Questions and Answers

G 1 S G 3 SG S G 19 1 AIPMT Pre 2012 17 A ring is made of a wire having a resistance Ro 12 2 Find the points A and B as shown in the figure at which a current carrying conductor should be connected so that the resistance R of the 2 3 4 8 sub circuit between these points is equal to 32 11 3 l 8 1 12 1 24 5103 N 00 00 2 8 VA 2 R 4 W S S G 1 12 V 2 6 V G S G R 18 If voltage across a bulb rated 220 volts 100 watts drops by 2 5 of its rated value the percentage of the rated value by which the power would decrease is 1 5 2 10 3 20 A 4 2 5 CE0144 In the circuit shown the cells A and B have negligible resistances For VA 12 V R 5000 and R 100 2 the galvanometer G shows no deflection The value of Va is CE0142 B 3 4 V CE0143 4 2V CE0145 ge is to be

A planet of mass m moves in an elliptical or bit around an unknown star of mass M such that its maximum and minimum distances from the star are equal to r and r respec tively The angular momentum of the planet relative to the centre of the star is b 0 a m c m 2GM2 1 1 2GM 1 7112 d 2GMmr 1 12 12

a 18 The earth 82 J cm radiation rate of receives solar min Assuming that the sun radiates like a blackbody calculate the surface temperature of the sun The angle subtended by the sun on the earth is 0 53 and the Stefan constant a 5 67 x 10 W m K Solution D Sun at R learth

34 A satellite of mass m orbit round the earth at a distance of 2 5R above its surface If gravitational field strength at surface of earth is g calculate the centripetal force acting on the satellite 1 3 mg 2 4mg 29 gi GM R2 mv DR 20 13 5 R 2 4 4mg 25 mg 25 sate Ma de max tu g 2 J25 27 1 r 3 57 E GM 8 5Y 8

How much below the surface of earth does acceleration due to gravity become 1 of its value at the earth s sur face The earth is assumed to be a sphere of radius 6 4 x 106 m 6336 km

29 The change in potential energy when a body of mass m is raised to height nR from the earth s surface is R is radius of earth 1 mgR 3 mgR n n 1 n n 1 2 nmgR 4 mgR 2 n n 2 1 Q O

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth i Determine the height of satellite above the earth s surface ii If the satellite is stopped suddenly in its orbit and allowed to fall freely on to the earth find the speed with which it hits the surface of the earth Take g 9 8 m s and 6400 km 7 92 km s 6400 km Re

A man of mass 90 kg is standing in an elevator whose cable broke suddenly If the elevator falls apparent weight of the man is 1 90 N 3 ON 2 90g N 4 any negative value

1 A satellite S is moving in an elliptical orbit around the earth The mass of the satellite is very small compared to the mass of the earth Then 1 the acceleration of S is always directed towards the centre of the earth 2 the angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant 3 the total mechanical energy of S varies periodically with time 4 the linear momentum of S remains constant in

1 If the gravitational potential due to the earth on its surface is assumed to be zero then gravitational potential at height 2R from surface will be Re Radius of the earth g acceleration due to gravity on earth surface 320e 1 3 gRe 3 2gRe 3 2 4 gR 3 2gRe 3 ft bg Re 3 At latitude 3 The escape sp escape speed twice the radi 1 2vo 3 2 18 The radii with de I am 3802 FRIR UR

If the distance between the sun and the earth is 400 times the distance between the moon and the earth and gravitational pull of the sun on the earth is 170 times the gravitational pull of the earth on the moon then the ratio of the mass of the sun to that of the moon is approximately equal to 1 2 7 107 2 4 6 10 3 6 8 10 4 7 4 x 104

33 There are two holes one each along the opposite sides of a wide rectangular tank The cross section of each hole is 0 01 m and the vertical distance between the holes is one metre The tank is filled with water The net force on the tank in newton when the water flows out of the holes is density of water 1000 kgm 1 100 3 300 2 200 4 400 als filled with

A rocket is fired vertically with a speed of 5 km s 1 from the earth s surface How far from the earth does the rocket go before returning to the earth Mass of the earth 6 0 x 1024 kg mean radius of the earth 10 11 N m kg 2 6 4 x 106 m G 6 67 NCERT 8 0 x 106 m from earth s centre

Two heavy spheres each of mass 100 kg and radius 0 10 m are placed 1 0 m apart on a horizontal table What is the gravitational force and potential at the mid point of the line joining the centres of the spheres Is an object placed at that point in equilibrium If so is the equilib rium stable or unstable NCERT 0 2 7 x 10 8 J kg an object placed at the mid point is an unstable equilibrium

lustration 21 A narrow tunnel is dug along the diameter of the earth and a particle of R distance from the centre Find the escape speed mass mo is placed at 2 of the particle from that place R 2

11 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 JEE Main 2019 10 Jan Shift 1 3 m b 2 mv c mv d mv a 2