Gravitation Questions and Answers

A satellite is launched from a point close to the surface of the earth radius R with a velocity v v1 5 where v is the velocity in a circular orbit It the initial velocity imparted to the satellite is horizontal the maximum distance from the surface of the earth during its revolution is NSEP 2018 1 R 2 2R 3 3R 4 4R

Two spherical planets P and Q have the same uniform density p masses Mp and Mo and surface areas A and 4A respectively A spherical planet R also has uniform density p and its mass is Mp Mo The escape velocities from the plates P Q and R are Vp Vo and VR respectively The A B VRVQ Vp VR 3 Vp C VQ VR VP DI Vp 1

Question No 76 Single Correct A A The weight of a body at the centre of earth is A 9 8 ms 2 B C D 0 4 9 ms 10 ms

Two identical magnetic dipoles of magnetic moments 1 0 A m each placed at a separation of 2m with their axes perpendicular to each other The resultant magnetic field at a point midway between the dipoles is A B skipped C D 5 x 10 7 T 5x10 T 10 7 T None of these 6 Correct MY PER SCO 4 out a

hary observer in space observes a system of binary stars undergoing circular motion about their centre of mass Because the observer is in the plane of the motion and is quite far away he sees both undergoing SHM with same angular frequency The velocity versus phase angle o rotated for both A B are shown below Take G 3 Observer 3 A MA 20 MB M RE R M A B If radius R 6 x 100 m M 2 x 100 kg Using data in option B M 9 x 100 kg B V 60 km s 40 km s 20 in option B time period T 6 28 x 10 sec x 10 Nm kg A B A 2A 6

A tunnel is dug along a chord of the earth at a perpendicular distance R 2 from the earth s centre The wall of the tunnel may be assumed to be frictionless Find the force exerted by the wall on a particle of mass m when it is at a distance x from the centre of the tunnel

l stion 3 After traveling a distance of 20 m along a transmission line the voltage wave remains 13 of it s source amplitude What is the attenuation constant of the 0 1 NP m 0 15 NP m 0 045 NP m 0 08 NP m O

22 When a maximum force of 3 N is applied on a body kept on rough inclined plane of shown in the figure then body remains stationary The maximum external force up the inclined plane that does not move the block is 12 N The coefficient of static friction between the block and the plane is Take g 10 m s a 3 ST 5 b 3NK 30 1 3 12 N C 3 3 LO 5 d 31 3 28 29

If Newton s inverse square law of gravitation had some dependence on radial distance other than which on of kepler s three laws of planetary motion would remain unchanged Olympiad Stage 1 2017 A First law on nature of orbits B Second law on constant areal velocity C Third law on dependence of orbital time period on orbit s semi major axis D None of the above

A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km Then the time period of a spy satellite orbiting a few hundred kilometers above the earth s surface REarth 6400 km will approximately be Rearth 6400 km A 1 2 hr B 1 hr C 2 hr D 4 hr Data hoight y from its surface Ifa in

Two bodies of mass m and M are revolving under the gravitational force of each other If they are moving in circular orbits of radii r and A respectively then which of the following option is correct A B D GMm 2 GMm R2 GMm rR 30 GMm R r mo r mo R Mo R mo

A planet of mass m revolves around the sun of mass M in an elliptical orbit The minimum and maximum distance of the planet from the sun are r r2 respectively If the minimum velocity of the 2GMr V 12 1 then it s maximum velocity will be planet is 2GMr V 1 B g 2GMr r r 2 2Gmr 1 r D 2GM 1

The figure shows an uniform slab of mass 7kg Find the moment of inertia about the axis normal to the plane of drawing and passing through the point O Given OA OC BC 10 cm and AB 2 cm C 90 R 168 kg cm2 2 cm B 10cm C 188 kg cm 2 D 198 kg cm

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

What will be the acceleration due to gravity at R a point which is at the distance 4 from Earth s centre R is radius of earth go is acceleration due to gravity at surface of earth Question Type Single Correct Type 1 2 3 90 4 3go 4 90 2

A body of mass m is projected horizontally just above the earth surface with velocity Vo ngR where R is the radius of earth If maximum height attained by the body from the surface of earth is 2R find the value of n m R M

QA planet of mass m is moving in an elliptical orbit round the sun of mass M If the maximum and minimum distances of the planet from the sun be 11 and 12 the angular momentum of the planet about the sun will be A B m GMm 11 1 1 1 m GMl1l2 C m 2GMl l 11 1

Question Two satellites are or biting Earth The path of one satellite has the equation x2 y2 56 250 000 The orbit of t he other satel Two satellites are orbiting Earth The path of one satellite has the

3 A satellite is revolving around earth with orbital speed vo If it stops suddenly then the speed with which it will strike the surface of earth is ve is escape velocity from earth s surface 1 e Vo 2 3 v e 2 Vo 4 2v

A solid block of mass 2 kg is resting inside a cube as shown in Fig The cube is moving with a velocity v 51 23ms 1 If the coefficient of friction between the surface of cube and block is 0 2 then the force of friction between the block and cube is A 10 N B 4 N C 14 N Zoro

If the escape velocity for an object placed at the surface of the earth is ve then the escape velocity for the same object when projected from the point of a tunnel made along diameter of t earth from a depth of d 0 05Re where Re is the radius of the earth is Less than ve by a factor of more than 5 Greater than ve by a factor of more than 5 Less than ve by a factor of less than 5 Greater than ve by a factor of less than 5

S on the pole of the earth its moment of inertia will 1 increase 2 decrease 3 remain unchanged 4 none of these 1 If the earth loses its atmosphere suddenly then the duration of day will 1 increase 2 decrease 3 remain unchanged 4 nothing can be definitely said

A planet is revolving around the sun in elliptical orbit with a semi major axis of 4 x 108 km Find the speed of the planet in km sec when it is at a distance of 2 x 108 km from the sun Given that Nm mass of sun is 2 x 1030 kg and universal gravitational constant is 6 67 x 10 11

Take the mean distance of the moon and the sun from the earth to be 0 4 x 106 km and 150 x 106 km respectively Their masses are 8 x 1022 kg and 2 10 0 kg respectively The radius of the earth is 6400 km Let AF be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and AF be the difference in the force exerted by the sun at the nearest and farthest points on the earth Then the number closest to AF is AF 1 2 2 10 2 3 0 6

A satellite is revolving close to the surface of earth What additional velocity is to be imparted to this satellite in the direction of its instantaneous velocity such that it overeomes the pull of earth M R is mass and radius of earth respectively A B C 4GM R 2 1 GM R GM

Inside a fixed sphere of radius R and uniform R density p there is spherical cavity of radius 2 such that surface of the cavity passes through the centre of the sphere as shown in figure A particle of mass mo is released from rest at centre B of the cavity Calculale velocity with which particle strikes the centre A of the sphere Neglect earth s gravity Initially sphere and particle are at rest A 2

A cavity of radius R 2 is made inside a solid sphere of radius R The centre of the cavity is located at a distance R 2 from the centre of the sphere The gravitational force on a particle of mass m at a distance R 2 from the centre of the sphere on the line joining both the centres of a sphere and cavity is opposite to the centre of gravity Here g GM R where M is the mass of the sphere A B C mg 2 3mg 8 mg 16

The figure represents a solid uniform sphere of mass M and radius R A spherical cavity of radius r is at a distance a from the centre of the sphere The gravitational field inside the cavity is A non uniform a R towards the centre of the cavity c directly proportional to a

A satellite is moving around the earth with speed v in a circular orbit of radius r If the orbit radius is decreased by 1 its speed will MP PET a Increase by 1 b Increase by 0 5 c Decrease by 1 d Decrease by 0 5

20 A satellite is moving in a low nearly circular orbit around the earth Its radius is roughly equal to that of the earth s radius R By firing rockets attached to it its speed is instantaneously increased in the direction of its motion so that it 3 becomes times larger Due to this the V2 farthest distance from the centre of the earth that the satellite reaches is R Value of Ris a 4Re c 3 Re b 2 5 R d 2R

A thin uniform annular disc see figure of mass M has outer radius 4R and inner radius 3R The work required to take a unit mass from point P on its axis to infinity is A 4 2 5 C 2GM 7R GM 4R 3R B P D 4R 4R 2GM 7R 2GM 5R 4 2 5 2 1

origin of co ordinate system lies at the centre of mass the sum of the moments of the masses of the system about the centre of mass a may be greater than zero b may be less than zero c may be equal to zero d is always zero 5 The centre of mass of a body is defined as the point at which the whole of its mass is supposed to be concentrated while centre of gravity of a body is defined as the point at which whole of its weight is supposed to be concentrated then a the centre of gravity always coincides with the centre of mass Rotate b the centre of gravity may lie slightly below the centre of mass c the centre of gravity may lie slightly above the centre of mass

In Fig 13 37 a particle A is fixed in placed at x 0 20 m on the x aixs and particle B with a mass 1 0 kg is fixed in place at the origin particle C are not shown can be moved along the x axis between particle B and x Figure 13 37b shows the x component Fnetx of the net gravitational force on particle B due to practices A and C as a functional of position x particle c The plot actually extend to the right approaching an asymptote of 4 17 x 10 0 Nas N as x what are the masses of a particles A and b particles C A BO a x Fnet x 0 0 2 Figure 13 37 Problem 12 0 4 06 08 x m b

hree point masses each of mass m are kept at the corners of an equilateral triangle of side L The system rotates about the center of the triangle without any change in the separation of masses during rotation The period of rotation is directly proportional to cos 30 sin60 3 2 3 A L B L C L 2 D L

7 An open elevator is ascending with constant speed 10ms A ball is thrown vertically upwards by a boy on the lift respect to the elevator The time taken by the ball to meet the elevator again is Velocity is 30maw 1270

A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth After it reaches height R R radius m of the earth it ejects a rocket of mass SO 10 that subsequently the satellite moves in a circular orbit The kinetic energy of the rocket is G is the gravitational constant M is the mass of the earth 1 20 2 Sm 3 4 3m m u 2GM 3R 119 GM 200 R 5GM 6R 2 113 GM u

A spherical shell is cut into two pieces along a chord and separated by large distance as shown in figure For points A and B where E and V are gravitational potential and field respectively A V V and EHEI B B V V and EHEI C V V and E HEI P Y Y and E KEI A

If a body is released from a point at a height equals to times the radius of the earth R its velocity equal reaching the surface of the earth is ng R 1 V 1 2 V 3 4 V 2ng R n 1 ng R 2 n 1 n 1 g R 2n

A small particle is dropped from a height R in front of a narrow tunnel dug inside the earth along a diameter Let M be the mass of earth R be radius of earth Let Vo I be speed of particle when it reaches A and time taken by particle to go from A to B respectively Assuming mass of particle to be negligible as compare to mass of earth pick the correct option s A C D B D GM 2R ka GM R R 2 GM T R

4 Stoj Body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity If R is radius of the earth the maximum height attained by the body is 1 R 6 2 R 3 3 2 3 4 R 60 Kep 1 c 2 3 4

SolveLancer Test Suppose a planet x has g 20 m s and planet y has g 5 m s A spaceship moves from y to x It has a mass of 1 kg attached to a spring balance The space ship move with constant velocity then reading of spring balance can be represented by which curve as a function of time 201 N a I b II c III III IV 1 II SolveLancer Test

A satellite is revolving very close to the earth surface in a circular orbit has potential energy U Find the change in its mechanical energy if it is made to move away from earth such that its velocity becomes half while going around the earth in a larger circular orbit 1 Zero 2 3 1 U 4 U 4 3U

A rectangular coil ABCD is hung from one hung from one side of a balance as shown in figure A 500 g mass is added to the other arm to balance the weight of the coil A current of 9 8 A is passed through the coil and a constant magnetic field of 0 4 T acting inward in xz plane is switched on such that only arm CD of length 1 5 cm lies in the field The additional mass m must be added to regain the balance is 1 4g 2 5g 3 69 500 g m B DxxC X X X X XX e I A B 100 m g x l 9 8 x 2 to 241x

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

gestion No 8 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 b O 1 1 01 4 O 3 1 O 2 1

The diagram shows three concentric conducting spherical shells having radii R 2R and 3R The initial potential of each she is as mentioned in the figure If the inner most shell is earth then the charge present on its outer surface would be equal to zero O 40TEOR O 4TTER O TER 10V 15V 30V

A large number of identical point masses m are placed along x axis at x 0 1 2 4 The magnitude of gravitational force on mass at origin x 0 will be 1 Gm y 3 213 Gm 2 Gm 4 4 Gm m mm x 0 x 1 x 2 m x 4 and so on

A coil of single turn is wrapped around a sphere of radius r and mass m The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere If the sphere is in rotational equilibrium the value of strength of uniform magnetic field in vertically downward direction is current in the coil is I as shown in figure 1 3 mg Tr mg C 2 00 mgsine Tlr 4 None of these

The tidal waves in the sea are primarily due to The atmospheric effect of the earth The gravitational effect of the moon on the earth Solar radiation on the earth Both 1 and 3

1 In the following four i Time period of revolution of a satellite just above the earth s surface T ii Time period of oscillation of ball inside the tunnel bored along the diameter of the earth Tma iii Time period of simple pendulum having a length equal to the earth s radius in a uniform field of 9 8 newton kg Tp iv Time period of an infinite simple pendulum in the earth s gravitational field T Which of the following is true 1 T T 2 T T ma st 1