Gravitation Questions and Answers

Acceleration due to gravity on moon is 1 6 sec An inflated balloon is released on moon It will 1 Move down with acceleration 1 6 m s 2 Move up with acceleration 1 6 m s 3 Move down with acceleration 9 8 m s 4 Move down with acceleration 9 8 m s

The time period of geostationary satellite at a height 36000 km is 24 h A spy satellite orbits earth at a height 6400km What will be the time period of sky satellite Radius of earth 6400 km O Sh O 4h 1 00 29 O 3h

Time speed of revolution of a nearest satellite around a planet of radius R is T Period of revolution around another planet whose radius is 3 R but having same density is O T O 3T OT

A body of mass m kg starts falling from a point 2R above the earth surface Its kinetic energy when it has fallen to a point upto height R above the earth s surface will be Mass of earth is M and its radius is R A B C GMm 2R GMm 6R 2GMm 3R GMm 3R

As shown in the figure a uniform rod of length 1 is sliding along two mutually perpendicular axes If the velocity of end B is VB 2 4 m s in the position shown then determine the velocity of end A Take cos 37 0 8 sin 37 0 6 O 37 A 1 8 m s B 2 0 m s c 3 m s V B

An astronaut orbiting the earth in a circular orbit 120 00 above the surface of earth gently drops a spoon out of space ship The spoon will O Fall vertically down to the earth O O Move towards the moon Will move along with space ship Will move in an irregular way 112 th

Solar energy reaches the earth at the rate of about 1 4 kW per square meter of surface perpen dicular to the direction of the sun Fig 1 15 By how much does the mass of the sun decrease per second owing to this energy loss The mean radius of the earth s orbit is 1 5 x 10 m Figure 1 15 1 4 kW m2 Solar radiation

Determine the work done in moving a body of mass m 100 kg slowly from the earth s surface to the infinity Take g 10 m s Radius of earth 6400 km A 6 4 108 J B 3 2 108 J C 6 4 10 J

Q 5 O 4 A point mass is placed inside a thin spherical shell of radius R and mass M at 202 1 a distance R 2 from the centre of the shell The gravitational force exerted by the shell on the point mass is GM 2R 00 26 000

secured at point Ex A particle of mass m and charge q is attached to a light insulating thread Exactly below point O there is a small ball having charge Q fixed on an insulating horizontal surface The particle remains in equilibrium vertically above the ball with the string taut Distance of the ball from point O is L Find the minimum value of Q for which the particle will be in a stable equilibrium for any gentle horizontal push given to it q L L

If both the masses and radius of the earth each decreases by 50 the acceleration due to gravity would O Remain same O O O Decrease by 50 Decrease by 100 Increase by 100

The acceleration due to earth s gravity on a point particle at a height h above the surface of the arth is denoted by 9 h and at a depth d below the surface of the earth is denoted by 9 d Consider the earth to be a sphere of radius R with uniform mass density Which of the following orrectly represents the ratio g d 9 d X 1 X 2 3 X 4 p 6 p 6 p 6 p 6 1 25 p 6 p 6 1 00 0 75 0 50 0 25 0 00 0 00 0 25 0 50 0 75 1 00 d R 1 00 0 75 0 50 0 25 0 00 0 00 0 25 0 50 0 75 1 00 1 25 d R p 6 p 6 1 25 1 00 0 75 0 50 0 25 0 00 0 00 0 25 0 50 0 75 1 00 d R 1 25 1 00 0 75 0 50 0 25 0 00 0 00 0 25 0 50 d R 0 75 1 00

In the arrangement of capacitors shown in Fig 3 63 the capacitors are initially uncharged and 200V now are connected with switch S open Find the potential of point b and the amount of charge 6 F a 66 7 V 300 C c 100 V 300 C 3 F H S 3 F HH b Fig 3 63 flowing through the switch when it is closed 6 F b 66 7 V 400 C d 133 3 V 400 C V 0

15 Example 8 A square of side 4 cmand uniform thic divided into four equal squares as shown in Fig 7 11 If one of the squares is cut off find the position of the centre of mass of the remaining portion from O 3m 9 OC AC 1 114 B Fig 7 11 Solution Let mass of each small square be m Total mass of the square will be 4m which acts at its centre of mass O Let O be CM of cut off square shaded square of mass m and O be CM of the remaining unshaded portion of mass 3 m Now AB BC 4 4 4 2 cm 4 2 2 2 2 cm 1 2 2 00 0c OC 2 cm 2

There are three planets in circular orbits around a fixed star at distances a 4a and 9a respectively in same sense say anticlockise At time t 0 the star and the three planets are in a straight line The period of revolution of the closest planet is T What minimum time after t 0 will they again be in the same straight line D ST 27 T

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively If TA and Tg are the time periods of A and B respectively then the value of TB TA B Given radius of earth 6400 km mass of earth 6x1024 kg 1 1 33 x 10 s 2 4 24 x 103 s 3 3 33 x 10 s 4 4 24 10 s

Choose the correct option The value of acceleration due to gravity is

Questions 8 10 Planet A 2Kx B Kx C D 4R Identical satellites X and Y of mass m are in circular orbits around a planet of mass M The radius of the planet is R Satellite X has an orbital radius of 3R and satellite Y has an orbital radius of 4R The kinetic energy of satellite X is Kx KN 2 Kx 2 3R 8 In terms of Kx the gravitational potential energy of the planet satellite X system is Purcha van Ras Ja ne persons Varund C House NO 186 121000 F

divisions which match with 16 main scale division The least count of the vernier calipers is 1 0 02 mm 2 0 2 mm 3 0 8 mm 4 0 08 mm 9GM where M is the mass of the earth and Ris A body is projected up with a velocity equal to 8R the radius of the earth The maximum distance it reaches from the centre of the earth is 9R 1 10R 9 2 8 16R 7 3 10R 3

sider 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 1 4Gm 3 3 26m 2 Gm 3 4 G

In case of an orbiting satellite if the radius of orbit is decreased Answer A B C Your Attempt its KE decreases its PE decreases Its ME decreases Correct answer

If the period of the planet Neptune is 165 0 Earth years what is its orbital radius Ans 4 50x10 2 m If the Earth be at one half of its present distance from the Sun how many days will be there in a year Ans 129 days

A satellite is revolving in a circular orbit of radius 2R R radius of earth The plane of the orbit is in equatorial plane and the direction of rotation of the satellite is opposite to the direction of spin of earth If T be the time period of rotation of earth around its own geometrical axis then time period of rotation of the satellite with respect to an observer on the surface of earth on its equator is 1 T 2 2x R g 3 2RT R T 9 2T R T R 2 zr R T g 4 2 T R 2 27 R T G

3 If the earth stops rotating the apparent value of g on its surface will a increase everywhere b decrease everywhere c remain the same everywhere d increase at some places and remain the same at some other places

A particle of mass m moves in response to a central force according to Newton s second law mr f r Show that F x c where is a constant vector The geometric interpretation of this leads to Keple second law Note Analytical mechanics notations were used der and deta Hint Show that m 0 dt d F dt This equation represents the conservation of angular momentum I defx mv

3 External torque is zero 4 All of these 10 If density of earth is p radius is R then its gravitational field at distance from centre will be 1 3 GpR 3 nGpR 2 4 Re 4 TGpR 12 GpR 6

ng 115 A body weighs 72 N on the surface of the earth What is the gravitational force on it at a height equal to half the radius of the earth 32 N 30 N 24 N 48 N 7 172 7 72 1 2 3 4 9 g 1 3 mg 272 R 79 Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 116 19

e escape velocity of a body projected from thesurface of earth is v If the body is projected at an angle to the horizontal surface of earth then the escape velocity would be B v cose A Ve C Ve Cos 0 D Ve sin 0

at distance r 2r 4r 8r and so on form a reference point O The gravitatonal field intensity at O will be A C GM r 2GM 3r B D GM 3r 4GM 3r

14 Satellite X moves around Earth in a circular orbit of radius R Satellite Y is also in a circular orbit around Earth and it completes one orbit for every eight orbits completed by satellite X What is the orbital radius of satellite Y A R B R C 2R D 4R E 8R

10 In the following two exercises choose the correct answer from among the given ones The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow see Fig 8 12 i a ii b iii c iv 0 78 Ab FR f Ca c Fig 8 12

D A block of mass M is hanging over a smooth and light pulley through a light string The other end of the string is pulled by a constant force F The kinetic energy of the block increases by 20 J in 1 s a The tension in the string is Mg b The tension in the string is F c The work done by the tension on the block is 20 J in the above 1 s d The work done by the force of gravity is 20 J in the abora 1

4 A rocket has landed on Planet X which has half the radius of Earth An astronaut onboard the rocket weighs twice as much on Planet X as on Earth If the escape velocity for the rocket taking off from Earth is vo then its escape velocity on Planet X is A 200 B 20 C Vo D vo 2 E v 4

The kinetic energies of a planet in an elliptical orbit about the Sun at positions A B and C are KA KB and Kc respectively AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure Then NEET 2018 B A S 1 KA KB Kc 2 KA KB Kc 3 KB KA Kc

27 A planet is moving in an elliptical orbit around the sun If T V E and L stand respectively for its kinetic energy gravitational potential energty total energy and magnitude of angular momentum about the centre which of the following is correct 1 T is conserved 2 V is always positive 3 E is always negative 4 L is conserved but direction of vector L changes continuously

18 A uniform metal ring of mass m and radius r is placed directly above a uniform sphere made up of same metal of mass M and of equal radius The centre of the ring is directly above the centre of the sphere at a distance 2 2r as shown in the figure The gravitational force exerted by the sphere on the ring will be 3GMm A 8r D GMm 10r B C 3 3 GMm 8r GMm 8r 3 2 2r 3

A clock S is based on oscillation of a spring and a clock P is based on pendulum motion Both clocks run at the same rate on earth On a planet having the same density as earth but twice the radius a S will run faster than P b P will run faster than S c They will both run at the same rate as on the earth d None of these

length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table If g is acceleration due to gravity the minimum work required to pull the hanging part of the chain on the table is 1 MgL MgL 2 LAX MgL 3 MgL

37 R is the radius of earth and is its angular a velocity and ge is the acceleration of gravity at equator The effective value of acceleration due to gravity at the latitude 30 will be equal to what 1 9E 30 R ge 4 M R 3 2 gE R 4 w R

A body of mass m is situated at distance 4Re above the Earth s surface where Re is the radius of Earth How much minimum energy be given to the body so that it may escape Question Type Single Correct Type 1 mgRe 2 2mgRe 3 mgRe 5

35 The height h at which the weight of a body will be th same as that at the same depth h from the surface of the eart is Radius of the earth is R and effect of the rotation of the eart is neglected 2 Sept 2020 Evening A C 5R R 2 R 2 B D 5 TC 2 R R 3R R 2

Three satellites are circling around the earth one along the circular orbit and the other two along elliptical orbi whose major axes are equal to the diameter of the circular orbit The masses of the satellites are same Choos the CORRECT options OOT Satellite 2 Satellite 1 A Energy is same for all the satellites B Angular momentum of satellite 1 is maximum C Angular momentum of satellite 2 is more than satellite 3 D Energy of satellite 1 is more than satellite 3 Satellite 3

loating the duration of the day would be approximately Take g 10 ms 2 the radius of earth R 6400 10 m Take 3 14 1200 minutes 84 minutes does not change 60 minutes Question Type MCQ Question ID 86435 Option 1 ID 86435

The acceleration due to gravity on the earth s surface at the poles is g and angular velocity of the earth about the axis passing through the pole is w An object is weighed at the equator and at a height h above the poles by using a spring balance If the weights are found to be same then h is h R where R is the radius of the earth

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 2 decrease by 2 4 increase by 1 1 decrease by 0 5 3 increase by 0 5

Two particles with mass of 1 kg and 2 kg initially at rest start moving towards each other due to mutual gravitational force of attraction If the initial distance between them is x then the distance covered by smaller mass when they meet will be 1 x 2 3 x 3 2 2x 3 4 x 4 f ma F a

The following figure shows two shells of masses m and m The shells are concentric At which point a particle of mass m shall experience zero force 1 A 3 C m m2 C B A 2 B 4 D

If three uniform spheres each having mass M and radius R are kept in such a way that each touches the other two the magnitude of the gravitational force on any sphere due to the other two is 1 3 GM 4r 2GM 2 2 4 2GM 2 3GM 2 4r

a point below the surface of earth equal to half the radius of earth R to a height R above the earths surface then work done on it will be a 5 6 mgR of 3

a m m m m Four point masses each of mass m are placed on the corner of square of side a Calculate magnitude gravitational force experienced by each particle