Gravitation Questions and Answers

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 TB are the time periods of A and B respectively then the value of TB TA mathongo mar mathe mat E B mathongo mathongo mathonge mathongo mathonne mathongo mathonje mathongo mathonga mathorgo mathongo mothor mathangamathongs mathonge Given radius of earth 6400 km mass of earth 6 x 1024 kg mathongo 1 4 24 x 10 s 2 3 33 x 102 s mathon mathongo moth

9 A black hole is an object whose gravitational field is so strong that even light cannot escape from it To what approximate radius would earth mass 5 98 x 1024 kg have to be compressed to be a black hole

As we know that the weight what we feel is th e counter force but during free fall counter for ce by crust would not be in concern but count er force by air is present that s the force by wh at we come down should be repelled by air wi th same force but yet we feel weightless wh y And if air applies counter force then they both should be cancelled out but yet we come dow n upon the crust why

Centre of gravity of a body on the earth coincides with its centre of mass for a small object and for a large object it may not What is qualitative meaning of small and large in this regard For which of the following two of them coincides a building a pond a lake a mountain NCERT Exemplar

A body of mass m is raised from the surface of earth to a height equal to radius of earth R If acceleration due to gravity on the surface of earth is g then gain of its potential energy is 1 mg 2 2mgR 3 mgR 4 mgR 2

16 Two planets revolve with same angular velocity about a star The radius of orbit of outer planet is twice the radius of orbit of the inner planet If T is time period of the revolution of outer planet find the time in which inner planet will fall into the star If it was suddenly stopped 1 T 2 8 T 2 2 4 T 2 16 T 2

1 The resistance of an ammeter is 132 and its scale is graduated for a current upto 100 A After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto 750 A by this meter The value of shunt resistance is AIPMT Prelims 2007 2 20 92 4 0 2 Q e 1 2 k 3 22

The Saturn s Moon x is having the gravitational acceleration on its surface as 5 m s and the another moon x is having the 4 of the radius of moon x and of the mass of moo x Find the magnitude of the gravitational acceleration at its surface ignoring the gravitational acceleration of Saturn a m s 32 b m s 16 c m s 16 3 d m s 32

R 55 Two point masses of mass m each are released from a very large separation They start to move towards each other The kinetic energy of one mass with respect to other when separation between them is r will be Juhal 4Gm F 1 72Gm r Gm 2 r Gm

interactic betwe The potential energy arc of ring of radius R and mass m and the particle of mass m placed at centre of curvature is M 1 3 GMm R 5 GMmo 6 R 60 mo 2 4 GMm 6R GMm 2R

D Find the percentage decrease in the acceleration due to gravity when a body is taken from the surface of earth to a height of 64 km from its surface Take R 6 4 106 m Hint Use 9 g 1 2h P

Two satellites of mass m and m m m ar going around the earth in orbits of radius r and r r r Which statement about their velocities correct 1 V V 3 V lr V lr 2 V V 4 V V

9 A network of four capacitors of capacity equal to C C C 2C C3 3C and C 4C are connected to a battery as shown in the figure The ratio of the charges on C and C is 4 1 22 3 G2 BC FC 3 30 C 20 HH CA lv C C AIPMT Prelims 2005 2 3 22

Hint Use Newton s universal law of gravitation P If the distance between earth and sun is increased by 2 then find percentage cha gravitational force acting between them Hint Use Newton s universal law of gravitation

44 The imaginary angular velocity of the earth for which the effective acceleration due to gravity at the AMU 2012 equator shall be zero is equal to 2 Take g 10 ms for the acceleration due to grat if the earth were at rest and radius of earth equal to 6400 km a 1 25 x 10 rad s 1 c 3 75 x 10 3 rad s 1 15 The maga of the maom b 2 50 10 rad s 1 d 5 x 10 rad s 1 ia 1 91 1234 56 5 6 B N A

41 A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R If the satellite is intended to move in a circular orbit of radius 7R the minimum energy

An experiment is performed on a puck on a level air hockey table where friction is negligible A constant horizontal force is applied the puck and the puck s acceleration is measured Now the same puck is transported far into outer space where both friction and gravity are negligible The same constant force is applied to the puck through a spring scale that stretches the same amount and the puck s acceleration relative to the distant stars is measured What is the puck s acceleration in outer space Make sure to explain your answer Total Marks K 10 T 5 C 10 A5

18 A planet has twice the mass of earth and of identical size What will surface of the planet where its acceleration due to gravity reduces by 36 of its value surface Hint Use g GM R and 9h 9 R R h

The diameter of sun is 1 39 x 10 m distance of sun from earth is 1 496 10 The angular diameter of sun is INCERT P k JIT JEE F 1 1290 2 9210 3 2190 4 1920

20 Find the percentage decrease in the acceleration due to gravity when a body is taken from the surface of earth to a height of 64 km from its surface Take R 6 4 x 106 m Hint Use 9 g 1 2h R

At what altitude the acceleration due to gravity reduces to half of its value as that of the earth Take radius of earth as 6 4 x 106 m g on the surface of the earth as 9 8 m s

36 ii Reduces by 36 of its value on the surface of earth Take R 6400 km much below the surface of the earth does the acceleration due to gravity i Reduces e Hint Take g gi 1 91 9

4 The escape velocity on earth is 11 2 kms If the onbody is projected out with twice this velocity then the speed of the body far away from the earth ignoring the presence of any other object in universe will be MP PET 2013 a 11 2 kms 1 c 19 4 kms 1 b 22 4 kms d 15 2 kms 1 1

EXAMPLE 16 Transferring the Satellite A 400 kg satellite is in a circular orbit of radius 2R about the earth How much energy is required to transfer it to a circular orbit of radius 4R What are the changes in the kinetic and potential energies INCR Sal 1

26 Two bodies of m and 4m are placed at a distance r The gravitational field is zero at a point on the line joining the two masses What will be the gravitational potential at this point AIEEE 2011

1 Earth is moving around the sun in elliptical orbit as shown The ratio of OB and OA and R Then the ratio of earth s is velocities at A and Bis a R 1 VOUS Sun KCET 2013 d R2 3 B ister b R c R if nodii R and R have densities d ation

Q 28 Average density of earth a does not depend on g directly proportional to g c b d is a complex function of g inversely proportional to g

For Question 21 25 two statements are given one labelled Assertion A and other Reason R Select the correct answer to these Question from the codes a b c and d as given below Both A R are true R is correct explanation of A Both A R are true but R is NOT the correct explanation of A A is true but R is false A is false R is true Assertion Reason Q 22 Assertion a b c d Q 21 Reason Q 23 Assertion Reason Classical Physics deals mainly with macroscopic phenomena The macroscopic domain includes atomic molecular and nuclear phenomenon When a solid is immersed in a fluid then a contact force develops in upward direction known as buoyant force which is equal to the weight of the fluid displaced A contact force on an object arises due to contact with some other object solid or fluid Satellite are always at finite distance from the earth Energy of satellites is positive or zero

Q 27 What is the gain in potential energy of an object of mass m raised from the surface of earth to a height R Acceleration due to gravity at the surface of earth g Radius of earth R mgR b mgR d a c 2mgR mgR

particle each of mass m move along a circle of radius R under the action of their mutual attraction The speed of each gravitational particle is 3 2Gm R 1 3 Gm V 2 R 2 fo 2 2 1 Gm R Gm 2 2 1 2 1 4 VR

Three identical point masses each of mass 1 kg lie a three points 0 0 0 0 2 m 0 2 m 0 The ne gravitational force on the mass at the origin is 1 6 67x 10 N 92 91 67 67x 10 N 3 1 67x 10 1 i N

photon is NCERT Pg 398 2 0 02 eV sm1 4 0 04 eV sm it rest decays into two 3m The ratio of de wwo particles will be INCERT Pg 4001 19 If the momentum of an electron is changed by P then the de Broglie wavelength associated with it changes by 0 5 The initial momentum of electron will be 1 200P P 200 INCERT Pg 400 2 400P 4 100P

108 If orbital speed of a satellite orbiting near of the earth in circular orbit is changed from V to 1 1V then it will Revolve in a circular orbit of larger radius 2 Follow a parabolic path 3 Revolve in an elliptical orbit M 4 Follow hyperbolic path

2 If the law of gravitation instead of being inverse square law becomes an inverse cube law then the true statement is 38 1 Circular orbits of planet is not possible 218 2 Projectile motion on the earth s surface will be circular 3 Planets will not have elliptical orbits YA All of these

134 Gravitation 105 A tunnel has been dug through a diamete solid sphere of uniform mass density Which graph best represents the variation of gravitational field intensity E with position r as one moves from A to B 1 3 E A B E L 1 hincos 2 2 K M M M E 4 106 An artificial satellite is moving in a circular orbit around earth has a kinetic energy anorou E 3 lepiley A 001 breol je bolovic

12 An object of mass M is divided into two parts which are placed at distance d If gravitational force of attraction is maximum between parts then find the ratio of mass of both parts

A hypothetical planet of mass m is moving along an elliptical path around sun of mass I under the influence of its gravitational pull If the major axis is 2R find the speed of the planet when it is at a distance of R from the sun ONO GM VR 2GMs R 2 GM R 27

4 106 86 A person can jump upto a height h RE earth Radius Rp of a planet on which the man escapes through jumping can be given by Density of planet is same as that of the earth and Reis radius of earth 1 Rp Rh 1 3 2 Rp REh 3 R 2R h R ne

56 Two point masses M and 4M are kept at a separation of 12 meter At what distance from the smaller mass The gravitational potential has a minimum magnitude 1 3 m 3 2 4 m dy dy 0 2 4 m 4 6 m 1

38 If the gravitational acceleration at s Earth is g then increase in potential lifting an object of mass m to a heigh half of radius of earth from surface mgR 2 mgR 1 2 2mgR 3 mgR

Two electrons of mass m each orbit around a nucleus of mass 80m such that both the electrons are always at the two diametric opposite points in their single circular orbit around the nucleus The ratio of gravitational force between an electron and the nucleus to that between the two electrons is K What is the value of K Backspace

8 Two particles each of mass M are released from rest when they are at infinite separation The velocity of any one when their separation becomes r will be 1 GM 2r GM 2 2GM GM

Two spheres of mass M M are placed in gravitational force between two masses is F liquid is filled in space having specific grav around the masses the gravitational force is 1 F 2 5F 3 F 5

If the universal gravitational constant decrease uniformly with time then the path of earth aroun sun will be 1 Same as it was earlier 2 Spiral of decreasing radius 3 Spiral of increasing radius 4 Straight line

a Centre of gravity C G of a body is the point at which the weight of the body acts b Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius 15 c To evaluate the gravitational field intensity due to any body at an external point the entire mass of the body can be considered to be concentrated at its C G d The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C G of the body to the exis Which one of the following pairs of statements is correct 1 a and b 2 b and c

18 A Geostationary satellite is orbiting at a height of 6RE above the surface of earth The time period of another satellite at a height 2 5RE above the surface of earth is RE is radius of earth NCERT Pg 196 1 6 hours 2 6 2 hours 6 3 hours

17 A point mass m is placed inside a spherica shell of mass M and radius R Th gravitational force experienced by the poi avile of las mass is NCERT Pg 18 1 3 GMm R 2GMm R 4 2 GMm 2R 4 Zero

12 38 Gravitation 1 A satellite revolving around earth has 2 MJ then the binding energy of the satellite is NCERT Pg 196 potential energy 1 1 MJ 2 2 MJ 3 1 MJ 4 8 MJ 2 Starting from the centre of earth having radius RE the variation is acceleration due

5 The potential energy of a system of four particles each of mass m placed at vertices of a square of side a is NCERT Pg 192 Gm Gm 1 4 2 a a ns Gm 2 4

5 Three equal masses 2m each are placed at the vertices an equilateral triangle PQR What is the force acting on a mass m placed at the centroid G of the triangle What is the force on mass m if the mass at the vertex P is quadrupled 1 Take PG QG RG 1 m 2m AY PA2m G m 30 X R 2m