Gravitation Questions and Answers

A spherical planet of radius R has spherically symmetrical distribution of mass density varying as square of the distance from the centre from zero at centre to maximum value po at its surface The value of escape velocity of a mass m at the surface of planet is 4TG R 5 The value of acceleration due to gravity g varies inside the planet as cube of the distance from centre The value of escape velocity from surface is same as the escape velocity from another planet of same total mass radius but having uniform mass density The energy required to impart escape velocity to particles of masses m 2m at the surface of planet will be in ratio 1 2

A stone weighs 50 N at an altitude equal to radius of earth The ratio of weight of stone on earth surface to that at depth of half of radius of earth will be 1 1 1 4 3 1

A planet moving around the sun sweeps area A in 3 days A2 in 6 days and A3 in 2 days The relation between A A2 and A3 is A A A A2 A3 2A A2 3A3 4A A2 6A3 A 2A2 3A3 A

A particle is projected from the ground with a velocity V 52 203 ms The maximum height attained and the range of the particle are respectively given by use g 10 m s 5m and 20m 20m and 20 m 20m and 5m 10 m and 10m

If the total energy of a satellite is negative it means Satellite will escape along parabolic path Satellite will escape along hyperbolic path Satellite will escape along linear path Satellite is in bound orbit

If mass of a planet is M radius is x then the work to be don to slowly take a 2 kg mass from surface to a height 4x is 8GM 5x 2GM X 5GM X 4GM 3x

If the particle shown is the figure is GM V 2R it returns after time T If it is projected such that time period of revolution is 8T then what is maximum distance of the particle from the centre of the earth with orbital speed v 1 7R R h R 2 3R

In reference to geostationary satellite which among the following is correct It moves in a plane containing Greenwich meridian It moves in a plane perpendicular to equatorial plane Its altitude above the earth surface is 24000 m It moves in equatorial plane

As we move from centre of earth to a certain height above the surface the acceleration due to gravity Continuously decreases First decreases then increases First increases then decreases Continuously increases

The periods of revolutions of two satellites are 4 hours and 16 hours The ratio of their radii will be 16 8 24 1 346

Question 20 A ball of mass m is fired vertically upwards from the surface of the earth with velocity nue where ve is the escape velocity and n 1 Neglecting air resistance to what height will the ball rise Take radius of the earth as R OA R n B R 1 n Oc Rn 1 n D Rn

71 A particle would take a time t to move down a straight tunnel from the surface of earth supposed to be a homogeneous sphere to its centre If magnitus of gravity were to remain same as that on surface throughout the tunnel then this time would be t The ratio of will be Find n t 2 n

14 Two planets have same density but different radii The acceleration due to gravity would be 1 Same on both planets 2 Greater on the smaller planet 3 Greater on the larger planet 4 Dependent on the distance of planet from the sun

20 x 10 Nm kg 2 M 6 x 1024 kg R 6400 km wherever required 3 An object A of mass of 10kg is balanced on a sensitive physical balance by a standard 10 kg block Now a 1000 kg mass is placed below A at a distan of Im How much additional mass should be added onto the other pan for balancing the physical balance Assume that the 1000kg mass is on interacting with A and not the other pan Use G A 6 6 x 10 4kg B 6 66 x 10 kg Oc 6 6 x 10 kg OD 6 6 x 10 kg

SolveLancer Test Their is a planet of mass M around which a satellite revolve in an elliptical orbit and length of semi major axis is a and length of semi minor axis is b If at an instant the distance of satellite from centre of planet is x then find the speed of satellite at that instant SolveLancer Test a b c 2GM GM b 2GM GM a 2GM GM a

16 A particle is dropped in three tunnels ACB AEB and ADB through earth and takes time to reach at point B respectively t t2 and t3 A C E B Then which of the following relation is correct D is not the centre of the earth

A 10 kg block placed on a rough horizontal floor is being pulled by a constant force of 50 N Coefficien of kinetic friction between the block and the floor is 0 4 Find the work done by each individual force acting on the block over a displacement of 5 m F

SolveLancer Test Two planets X and Y orbit around sun in circular orbits Y completes 1 revolution around the sun in time t How many does X complete in time t Given that rx Ty 3r SolveLancer Test a 3 b 9 c 27 d 81

For the path PQR in a conservative force field the amounts work done in carrying a body from P to Q and fror Q to Rare 5 Joule and 2 Joule respectively The work done in carrying the body from P to R will be 1 7 J 2 3J R 3 21J 4 Zero

59 Two asteroids heavenly bodies of equal masses revolve diametrically opposite to each other in a circle of radius 100 km If mass of each asteroid is 1010 kg then what would their velocities be Take G 6 67 x 10 1 N m kg 2

II a A massless spring of rest length with no tension has a point mass m connected to one end and the other end fixed so the spring hangs in the gravity field as shown in Fig The motion of the system is only in one vertical plane Set Lagrangian equations of motion 9 Korogorosos 1 m

The gravitational force between two identical spheres is given as 8x10 5 N The spheres are separated by a distance of 0 53m at the center What is the mass of each sphere O 25 56 kg O 25 56 lb 5 80 210 kg O 5 80 10 lb

A planet moves around the sun At a point P it is closest to sun at a distance d and has speed v At another point Q when it is farthest from sun at distance d its speed will be 1 2 d 3 dzej di 4 d dv da di

The reading of spring balance when measuring weight of body is double at pole compared to the reading taken at equator of planet X If the velocity of a point at equator of planet is x then what is the escape velocity when body is projected from pole tangentially SolveLancer Test a 4x b x 2

A body projected vertically from the earth reaches a height equal to earth s radius before returning to the earth The power exerted by the gravitational force is greatest 1 At the highest position of the body 2 At the instant just before the body hits the earth 3 It remains constant all through 4 At the instant just after the body is projected

The gravitational potential due to 6 particles each of mass 2 kg placed at vertices of a regular hexagon of side length 6 m at the centre of hexagon is 9 6 x 10 14 J kg 14 1 x 106 J kg 2 1 x 10 8 J kg 13 2 x 10 11 J kg

The depth d at which the value of acceleration due to gravity is th of the acceleration due to gravity at altitude R from 4 surface of the earth is R radius of earth R 15R 16 2R 14R

If an object is projected vertically upwards with speed three times of the escape speed v from earth s surface then velocity of object in the interstellar space will be 1 2VE 2 2V 3 2 2V 4 VE Office Aakas

3 10 A cyclist rides along the circumference of a circular Horizontal plane of radius R the frictional coefficient being dependent only on distance r from the centre O of the plane as Ho 1 7 where u is a constant Find the radius of the circle with the centre at the point along which the cyclist can ride with the maximum velocity What is this velocity 1 Ans R 2 MoRg

Q 4 Escape velocity of a body of 1 kg mass on a planet is 100 m sec Gravitational Potential energy of the body at the Planet is Choose only 1 answer A 5000 B 1000 C 2400 Your Answer

In a certain universe the gravity is a conservative force but not necessarily an inverse square law force In that universe there exists a single point like mass m that is influenced only by gravity As a result of a gravitational force the mass orbits the fixed source point O in a circle so that the source point is on the circle s rim Neglecting the singular point select that correct alternative s r is the distance of m from O Vo P OP 2R 4R V A Velocity of the point mass as function of r is given by r 0 B Force experienced by point mass depends on intial speed V of point mass C Force experienced by point mass will be inversly proportnal to fifth power of its distance from O D Position vector of particle with respect to centre of circle sweeps out equal area in equal interval of time

c 14 ms d 5 Two stars of masses m and my distance r apart revolve about their centre of mass The period of revolution is a 2 c 2 2 2G m m 2r G m m b 2 d 2 P m m 2G mm G m m

Two wires of the same material have lengths in the ratio 1 2 and their radii are in the ratio 1 2 If they are stretched by applying equal forces the increase in their lengths will be in the ratio

ameter of change heated to copper has a error in the de a 0 9 b 2 4 c 23 A carpet of mass M made of an extensible material is rolled along its length in the form of a cylinder of radius R and kept on a rough floor If the carpet is unrolled without sliding to a radius R 2 the decrease in potential energy is MgR c MgR 8 b MgR 3 MgR d liquid of density P is filled in a wide tank to a lid rod of length L cross section A and the tank The lower

A particle is dropped in three tunnels ACB AEB and ADB through earth and takes time to reach at point B respectively t1 t2 and t3 Then which of the following relation is correct D is not the centre of the earth C A t t t3 E 1 13 B

A uniform string of large length L of uniform cross section mass per unit length and free at both ends is revolving round the earth at equator in vertical position in such a way that its position relative to mass of earth M radius R is always the same and its lower end is slightly above the earth s surface Potential energy of string is GMXen Net force exerted by gravity on string is GMAL R R L Angular velocity of revolution of string is R LY R Angular velocity of revolution of string is 2GM R R L 2R L 2GM R R L R 2L

Two Earth s satellites move in a common plane along circular orbits The orbital radius of one satellite is r while that of the other satellite is r Ar Here Ar r A Time interval separates the periodic approaches of the satellites to each other over the minimum distance B C D is 5 2 is 4 5 Time interval separates the periodic approaches of the satellites to each other over the minimum distance 2 r 5 2 3 GM 2 Ar 1 2 3 GM Ar Angular velocity of approach between two satellites is Angular velocity of approach between two satellites is 1 2 3 GM Ar 5 2 3 GM 1 2 Ar 5 2 2r

A planet of mass m revolves ar orbit of area A and eccentricity 0 5 1 3 SUN It moves between point P to Q in time At then the angular momentum of planet about the sun at perihelion is mA 24t P 2 14 mA At C centre of ellipse 2 4 1 07 mA At 1 57 mA At

14 The ratio of the energy required to raise a satellite upto a height R radius of earth from the surface of earth to that required to put it into orbit there is a 1 1 b 8 1 c 4 1 d 2 3

c 2R 17 The gravitational field in a region is given by E 41 i N kg Work done by this field is zero when a particle is moved along the line a y 4x 2 c x y 5 b 4y x 6 d All of these

The time taken by the light and its order of magnitude if travels a distance of 5 6 x 1025 m between two planets Speed of light c 3 x 10 m s A B D time taken by the light 1 87 x 10 7 s order of magnitude 10 17 time taken by the light 1 87 x 10 7 s order of magnitude 1018 time taken by the light 1 87 x 10 8 s order of magnitude 10 18 time taken by the light 1 87 x 1016 s order of magnitude 10 17

mtG Objective NCERT P 18 A spaceship is launched into a circular orbit close earth s surface The additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is Radius of earth 6400 km and g 9 8 ms a 11 2 km s 1

a a 2A X c b 16 A uniform ring of mass Mand radius Ris placed directly above a uniform sphere of mass 8 M and of same radius R The centre of the ring is at a distance of d 3 R from the centre of the sphere The gravitational attraction between the sphere and the ring is 8 GM R 2GM 3 R 3 GM R 3 GM 2R2 5 x b X d

31 Three solid spheres each of mass m and radius R are released from the position shown in figure The speed of any one sphere at the time of collision would be a Gm 1 c Gm 3 d R 1 Gm 2 1 R d 8 d d b Gm d d Gm 3 1 d R 1 R NIC 2

Example 10 8 A fully loaded Boeing aircraft has a mass of 3 3 x 105 kg Its total wing area is 500 m It is in level flight with a speed of 960 km h a Estimate the pressure difference between the lower and upper surfaces of the wings b Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface The density of air is p 1 2 kg m

A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M see figure The point masses are connected by a rigid massless rod of length 1 and this assembly is free to move along the line connecting them All three masses interact only through their mutual gravitational interaction When the point mass nearer to M is at a distance r 31 from M The value 288 M the tension in the rod is zero for m k of k is JEE Advanced 2015

Weight of a body at the equator of a planet is half of that at the poles If peripheral velocity of a point on the equator of this planet is vo what is the escape velocity of a polar particle a vo c 3v0 6 200 d 4v0

An asteroid orbiting around a planet in circular orbit suddenly explodes into two fragments in mass ratio 1 4 If immediately after the explosion the smaller fragment starts orbiting the planet in reverse direction in the same orbit what will happen with the heavier fragment a Fall on the planet b Start orbiting the planet in a larger orbit c Start orbiting the planet in a smaller orbit Escape from the gravitational interaction with the planet

10 Consider a thought experiment performed in free space In the experiment a small cube C of mass m is placed at the centre of a large and highly massive disc D and a ball B of mass M revolves in circula path of radius R around the centre of the disc The plane of the circle perpendicular to the plane of the disc as shown in the figure Intens of the gravitational field of the disc near its centre is g What should range of coefficient of friction between the cube and the disc so tha cube remains motionless a z gR SR GM GM GR GM c uz b uz gR R GM GM BR GM d u 2

Three identical point masses each of mass 1 kg lie in the x y plane at points 0 0 0 0 2 m and 0 2 m 0 The gravitational force on the mass at the origin is 1 67 10 i j N O 3 34 10 0 i j N O 1 67 10 i j N 3 34x10 0 i j N