Gravitation Questions and Answers

15 A particle is given an initial speed inside a fixed smooth spherical shell of radius 1 m such that it just able to complete the vertical circle acceleration of particle at instant when velocity becomes perpendicular to initial initially particle is at the bottom 1 10 g 2 g 3 2 g

Level 11 In the circuit shown the cells A and B have negligible resistances For VA 12 V R 500 and R 100 2 the galvanometer G shows n deflection The value of VB is 1 12 V R www ww R G AIPMT Prelims 2 6 V LAY 211

For a satellite escape speed is 11kms If the satellite is launched at an angle of 60 with the vertical what will be the escape speed 11 km sec because C escape speed R Radius of earth 2GM X No chan Ru Lox No change of earth Constant change

4 0 g of a gas occupies 22 4 lites at NTP The specific heat capacity of the gas at constant volume is 5 0 JK mol If the speed of sound in this gas at NTP is 952 ms then the heat capacity at constant pressure is Take gas constant R 8 3 JK mol 1 7 0 JK mol 1 3 8 0 JK mol 2 8 5 JK mol 1 4 7 5 JK 1 mol

A particle executes simple harmonic oscillation with an amplitude a The period of oscillation is T The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is a T 8 b T 12 c T 2 d T 4 2007

SolveLancer Test Consider the statements which of the following is correct SolveLancer Test a S is equal to the wave intensity Where symbol have their usual meaning b Curvature of a Comet Tail is due to the force of gravity e The resonant frequency of water molecules in food items always less than frequency of microwaves 1 d For a capacitor the charging current I and displacement current I can never be equal to each other i

33 A small drop of water falls from rest through a large height h in air the final velocity is IS Proportional to h 2 Proportional to h 3 Inversely proportional to h MPYAY Almost independent of h

17 m W math 09 NTA Test 09 Numerical There is a crater of depth on the surface of the moon where R is the radius of the moon A ball is projected vertically upwards from the crater with a velocity which is equal to the escape velocity from the surface of the moon If the R 100 thongo mathongo mathongo e mathoaximum height attained by the particle is close to nR where n is an integer then find the value of n honge mothongo

6 82 A massive body moving radially from a planet of mass M when at distance r from planet explodes in such a way that two of its many fragments move in mutually perpendicular circular orbits around planet Find the maximum distance between fragments before collision and their relative speed at the moment they collide 6 GM

spherical portion of radius Restic From a solid sphere of mass M and radius R a shown Find gravitational potential at of cavity M R 1 3 4GM R 3 GM 2 R siast Course Il 14 44 R 2 2 GM R 4 None of these M from 1 3 a fav 4GM R 3 GM 2 R Space for Rough Work fery Ge ya z u M fanger R feren aan een nahm M R R 2 2 4 Y GM R 1001CMD30222000 E H 0909202

1 28 N 2 16N 3 32 N 4 72 N Consider the following statements 36 S An object shall weigh more at pole than at equator when weighted by using a physical balance S It shall weigh the same at pole and equator when weighed by using a physical balance S It shall weigh the same at pole and equator when weighed by using a spring balance S4 It shall weigh less at the pole than at equator when weighed using a spring balance Which of the above statement is correct 1 S 2 S 3 S 4 1 28 N 2 16 N 3 32 N 4 72 N ffeferat framfort S feft aega tegell and at a gat e giar o S fat are at the end har en Syft Sfat eram ne question a 1 S ten af af 2 S that gall ar an nan vi gai den gell at 11 a 4 ya 3 Sy 4 SA

39 A particle of mass M is situated at the centre of a spherical shell of same mass and radius a The a magnitude of the gravitational potential at a point situated at distance from the centre will be 2 My fa feed far fare odia faxa en un am GM a 1 2 2GM a 3GM a 4 4GM a

R A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F Now a spherical cavity of radius 2 made in the sphere as shown in figure and the force becomes F The value of F F2 is A 36 25 B 41 50 of 3 B 2R m

A body weights 49N on a spring balance at the north pole What will be its weight recorded on the same weighing machine if it is shifted to the equator Use g A B 49 N GM 9 8 ms 2 and radius of earth R 6400 km R 49 83 N

6 57 A body on the equator of a planet weighs half of its weight at the pole The density of matter of the planet is 3 g cm Determine the period of rotation of the planet about its axis Ans 3 16 x 104 rad s X

In the equation of angular displacement of a particle moving on a circular path is given as 0 2t 0 5 0 is in radian and in second The angular velocity of the particle at t 2 s is 16 5 rad s 19 5 rad s 24 rad s 12 rad s

3 10cm 4 2 5cm A body of mass m is situated at distance 4R 13 above the Earth s surface where R is the radius of Earth how much minimum energy given to be the body so that it may escape 2 2mg mgR 16 1 mgR mgR 3 5 3 10cm 4 2 5cm me and years fear and R qoffroa atd ant fa 1 3 mgR mgR 5 2 2mg mgR 4 16

3 In ac circuit when ac ammeter is connected it reads i current If a student uses de ammeter in place of ac ammeter the reading in the de ammeter will be 1 1 2 2 i 3 0 637 i 4 zero

a large iron block rapidly back and forth She com pares that to her moving it on earth on a smooth horizontal surface She finds that 1 the shaking costs her no effort because there is no weight of block 2 the shaking costs her some effort but consid erably less than on Earth 3 the effort required is same is that on earth the shaking costs hor

7 State whether the following statements are true or false If zero of the potential energy is not at infinity even then total energy of an orbiting satellite is negative of its kinetic energy The force of attraction between a hollow spherical shell of uniform density and a point mass placed outside it is zero i The force of gravity is a conservative force O True True False True True True O False True True False False True

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a The gravitational potential at a point situated at 2 distance from the centre will be AIPMT Prelims 2010 A B 3GM a 2GM a

Assume that the mass density of the Sun is uniform and treat solar radiation as blackbody radiation It s given that the surface tem perature of the Sun is 6000 K and assume that the Sun continues giving energy at the same rate in future If the source of Sun s ra diated energy was its gravitational potential energy instead of the nuclear fusion then the Sun will cease to exist in a time of the order of x 10 years 2 10 million years 2 X3 1 billion years 3 X4 1000 years

A planet of mass m is revolving around the earth at a height of R from earth surface Speed of this satellite is V speed of another satellite of mass 2m and revolving at a height 3R from earth surface will be A B V 2 2V

Assuming that gravitational potential energy at the surface of earth is zero the change in gravitational potential energy of an object of mass m when taken to a height h from the surface of earth of radius R mass M is given by h R A B C D GMm R h GMm R h mgh mghR R h

A space ship is sent to investigate a planet of mass M and radius R While hanging motionless in space at a distance 5R from the centre of the planet the space ship fires an instrument package with speed vo as shown in the figure The package has mass m which is much smaller than the mass of the space ship For what value of angle 8 the package will just graze the surface of the planet B faydal 5 kaft v kat Vo afm sin M sin 5R sin 1 1 Correct Answer 1 M 8GM GR 8GM 5R kera 2 2GM 5 R

suppose two planets spherical in shape in radii R and 2R but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet The minimum speed v required for the satellite to reach the surface of the second planet is then the value of a is a GM 7 R Given The two planets are fixed in their position MR 9M 2R

A student performs an experiment for determination of l 9 47 0 and in time T is AT and n is number of times the reading is taken The measurement of g is most accurate for A B C Al 5mm AT 0 2sec n 10 The error in length lis Al Al 5mm AT 0 2sec n 20 Al 5mm AT 0 1sec n 10 se 1mm AT 900 50

elocity of point on the equator of rotating spherical planet is V The angular velocity of the planet is such that the value of g at the equator is alf of g at the pole The escape velocity for a polar particle on the planet is xV Find x

Consider an earth satellite moving with a speed 8200 m s at perigee which is 340 km above the earth s surface Calculate distance to the satellite from the earth s surface when t is at apogee Radius of earth is 6 4 100 m a 2340 km b 4580 km c 3520 km d 1850 km

Two astronauts are floating in gravitational free space after having lost contact with their spaceship The two will a move towards each other b move away from each other c will become stationary d keep floating at the same distance between them NEET 2017

15 C 8 m D 6 m 3 grooves AB AC and AD are made in a circular disk lying in a vertical plane 3 particles B C and D constrained to move along path AB AC and AD respectively are released from point A Particle B reaches point B in time te particle C reaches point C in time t and particle D reaches at point D in time to Then which of the following is incorrect s A te tc to te te to B te t to D to te tc B 25

All Questions are compulsory SECTION A Read the following passage carefully and answer the questions given below 10 Surrounded by the Vindhya ranges Bhimbetka caves lie 46 kms South of Bhopal Over 600 rock shelters belonging to the Niolithic age were discovered in the midst of a dense forest Here paintings in our 500 caves depict the life of the pre historic cave dwellers making Bhimbetka an archeological treasure Paintings are mainly in red and white with the occasional use of green and yellow The scenes usually depict hunting dancing music horse and elephant riders animals fighting honey collection decoration of bodies maskes and household scenes Animals such a bisons tigers lions bears elephants antelopes dogs lizards crocodiles etc have depicted in these caves Popular religious and other symbols also occur frequently The Superimposition of paintings shows that the some rock surface was used by different people at different times Questions 1 How for is Bhimbetika from Bhopal 2 Whose life is depticted in the painting 3 What are the colours used in these paintings I see in these paintings Q 1

If three particles each of mass M are placed at the three corners of an equilateral triangle of side a the net force exerted by this system on another particle of mass M placed at the mid point of any one side is 1 4GM 22 2 3GM 2 3 3GM 2 4 0

Correct Question No 19 Options h 90 5 R InCorrect A body is projected vertically upwards from the R bottom of a crater of moon of depth where Ris 100 the radius of moon with a velocity equal to the escape velocity on the surface of moon Calculate maximum height attained by the body from the surface of the moon 005 R UnAnswer

A satellite is moving with a constant speed V in a circular orbit about 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 its ejection the kinetic energy of the object is B D 2mV A 1 2 MV mv mV C 3 mV

Three masses each equal to m are placed at the three corners of a square of side 1 The magnitude of gravitational force on unit mass at the fourth corner will be B A Gm 31 3Gm 2 Gm www D 3Gm 12

The orbital velocity of an artificial satellite in a circular orbit just above the earth s surface is v For a satellite orbiting at an altitude of 3 4 of the earth s radius above its surface the orbital velocity is 3 C

Figure shows sun S such that the area of triangle csa is the area of the ellipse See figure With db as the semimajor axis and c as the semiminor axis Ift is the time taken for planet to g over path abc and to for path taken over cda then Online April 9 2016 d a t 4t S C a b b t 2t

81 A body is thrown vertically upwards with a velocity u It will fall back at a point displaced to the west by a distance 1 2 14h a c 3 g 2 8h 3 g 1 2 Cos o Cos b d 1 8h 3 g 4 8h 3 g 1 2 1 2 w cos o cos o

6 50 A projectile is fired vertically upward from the surface of earth with a velocity Kv where v is the escape velocity and K 1 Neglecting air resistance show that the maximum height e to which it will rise measured from the centre of earth is R 1 K where R is the radius of the earth

6 You are riding in an elevator that has an acceleration of 3 m s upwards Suppose your normal weight is 60 kg on level ground on the earth If you had a scale under your feet on the elevator what would the indicated weight be

16 A satellite S is moving in an elliptical orbit around the earth The mass of the satellite is very small as compared to the mass of the earth Then a the angular momentum of S about the centre of the earth changes in direction but its magnitude remains constant b the total mechanical energy of S varies periodically with time c the linear momentum of S remains constant in magnitude the acceleration of S is always directed towards the centre of the earth Explain which is more Two particles A and P Love with constant velocities v and v At the initial inomet 1

An electron is confined to a narrow evacuated tube of length 5 m the tube functions as a one dimensional infinite potential well a What is the energy difference between the electron s ground state and its first excited state b At what quantum number n would the energy difference between adjacent energy levels be 1 eV which is measurable unlike the result of a At that quantum number c what multiple of the electron s rest energy would give the electron s total energy and d would the electron be relativistic a Number i 0 0603e 18 b Number 3 32e19 c Number 0 32e14 Units Units Units eV This answer has no units This answer has no units

g A small solid ball is projected vertically up from 3 ground at a large initial speed u gR where g is acceleration due to gravity on the surface of the earth and R is earth s radius The maximum altitude upto which the ball will go is neglect air friction ask 3 Services Limited 2 4 Poundation R3 3R 4

on an inclined plane forming an angle a with the horizontal fig and is imparted an initial velocity vo Find how the velocity of the disc depends on the angle if the friction coefficient k tana and the initial moment 80 1 2 X VO

3 identical point particles of mass M move in such a way that distance between particles is which remain constant Only force is the gravitational force between particles Then magnitu of relative velocity in m s of one particle with respect to other particle will be Take GM 3 m s

v In a double star two stars one of mass m and the other of 2 m distance d apart rotate about their common centre of mass Deduce an expression for the period of revolution Show that the ratio of their angular momenta about the centre of mass is the same as the ratio of their kinetic energies

from the 1 centre field and potent 6 5 In figure 6 105 particle A has a mass of 1 4 kg and particle B has a mass of 3 1 kg What is the gravitational field at point P 1 5 m A 2 4 m Figure 6 105 B

A uniform chain of mass m rests on the quarter part of the sphere smooth with help of idea string as shown in the figure The tension in the string will be A mg T B mg R Fixed C m 2mg T D zero

The Earth has a circular orbit of radius r and period t around the Sun Mars has a circular orbit of radius R and period T In order to send a spacecraft from the Earth to Mars it is convenient to launch the spacecraft into an elliptical orbit whose perihelion coincides with the orbit of the Earth and whose aphelion coincides with the orbit of Mars this orbit requires the least amount of energy for a trip to Mars The time t taken by a spacecraft to reach Mars from the Earth satisfies Mars Sun