Gravitation Questions and Answers

Gravitation 39 3 An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body from the surface of earth The height of satellite above earth s surface is R is radius of earth 1 3R 3 7R 2 5R 4 8R 4 Which graph best reproconto

It will rer Suppose the Saturn rings consist of football size particles orbiting in circular orbits If the maximum speed of these particles is 1 05 times of the minimum speed find ratio of radial width to the inner radius of the ring a 0 01 c 0 10 b 0 05 d 0 25

0 O m 2m 0 For For 3mg k maximum tension in string is 4mg Smg k minimum tension in string is mg Frequency of osciliation of system in for all non zero values of xal 3mg

A ball is dropped from a spacecraft revolving around the earth at a height of 120 km What will happen to the ball a it will fall down to the earth gradually b it will go very far in the space c it will continue to move with the same speed along the original orbit of spacecraft d it will move with the same speed tangentially to the spacecraft 1996

A satellite revolve around the earth at a height 900 km above the surface of the earth in a circu orbit Calculate its orbital velocity G 6 67 x 10 11 Nm kg Mass of the earth 6 x 1024 radius of the earth 6400 km my 4MML

The radius of the earth is 6370 km and radius of mars is 3440 km What is the acceleration due to gravity on mars if mass of the mars is 0 11 times the mass of earth g G Me boll

3 times 12 mes 14 Imagine a narrow tunnel between the two diametrically opposite points of the earth A particle of mass released in this tunnel The time period of oscillation is 1 2 4 R 2 g 2 R

etween two point masses m and m placed at a distance r is given by object of mass M is divided into two parts which are placed at distance r Find the mass of both parts if gravitation force of attraction is maximum between them 1 Gmim where G is an universal constant An Gm m 3 M 2M w 3 3 3 MM 2 2 2 4 M 3M 4 4 M 4M 5 5

3 Consider 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 close orbit due to their mutual gravitational force c attraction 1 4Gm 3 2 Gm 3 2Gm

A planet moves around the sun along an ellipse so that its minimum distance from the sun is equal to r and the maximum distance to R Making use of Kepler s laws its perio find the value of n of revolution around the sun is given by T SRA 2a R r R r Gm THE

A ball is dropped down from the roof of a building and stimulus three are there ball is thrown in a horizontal direction when will the balls reach the ground a same time but different places b same time and same place

A ring of radius R 8m is made of a highly dense material Mass of the ring is mR 2 7 x 10 kg distributed uniformly over its circumference A particle of mass dense mp 3 x 10 kg is placed on the axis of the ring at a distance x 6m from the centre Neglect all other forces except gravitational interaction Determine speed in cm sec of the particle at the instant when it passes through centre of ring

A glass block measured 5 cm x 5 cm x 15 cm When block stands on one of its smaller faces and viewed directly from above it appear to be almost a cube Then find the refracting index of block

1 A jet airplane travelling at the speed of 500 kmh ejects its products of combustion at the speed relative to the jet plane What is the speed of the combustion with respect to a observer on ground 1500 kmh 2550 km h 2000 km h b d 1250 km h 1000 km h

33 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 a at the instant just before the body hits the earth b it remains constant all through c at the instant just after the body is projected d at the highest position of the body through diagram 1

s 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 a at the instant just before the body hits the earth b it remains constant all through c at the instant just after the body is projected d at the highest position of the body

A fixed sphere of radius R and charge Q uniformly has a small groove of length as shown in figure Another point charge of mass m and charge q is projected towards the groove with some 1 xQq velocity in given direction If maximum value of v so that it does not strike to sphere is 8VmRo then find x Neglect gravity Both charges are of same nature

2 2 Three point masses each of mass m rotate in a circle of radius r with constant angular velocity due to their mutual gravitational attraction If at any instant the masses are on the vertex of an equilateral triangle of side a then the value of wis a CR c V Gm 3 a Gm 3 3a ei noass b 3Gm 3 a d None of these

5 1 Three particles each of mass m are located at the vertices of an equilateral triangle of side a At what speed must they move if they all revolve under the influence of their gravitational force of attraction in a circular orbit a Va 2Gm circumscribing the triangle while still preserving the equilateral triangle 0102691 1922A Gm b c ch of mass m rotate in a circle due to a 3Gm m a Am d 4Gm B a m

If the angular speed of earth increases to n n times the present value then acceleration due gravity at poles 1 Increases to n2 times 2 Decreases to n times 3 Decreases to n times

Two particles A and B of mass 1 kg and 4 kg respectively approach each other due to their mutual gravitational force only Then the ratio of acceleration of A to B at any instant is 1 4 1 V 3 1 2 2 2 1 4 1 4

5 Infinite number of masses each of mass 3 kg are placed along the y axis at y 1 m 3 m 9 m 27 m The magnitude of resultant gravitational potential in terms of gravitational constant G at the origin y 0 is 1 4 5 G unit 3 3 G unit 2 G unit 4 9 G unit

size of earth starts from rest from h R above the earth s surface It reaches earth in time 2h 9 a t c t h 9 2h 3g b t d t 4h 2601 3g d to raise a satellite to

50 Four particles each of mass M move along a circle of radius R under the action of their mutual gravitational attraction The speed of each particle is a L c GM R GM 2 2 1 VR b 2 2 GM R GM 2 2 1 d VR are 1 CI

Example 8 5 The planet Mars has two moons phobos and delmos i phobos has a period 7 hours 39 minutes and an orbital radius of 9 4 x10 km Calculate the mass of mars ii Assume that earth and mars move in circular orbits around the sun with the martian orbit being 1 52 times the orbital radius of the earth What is the length of the martian year in days

A body is projected vertically up at t 0 with a velocity of 98 m s Another body is projected from the same point with same velocity after time 4 seconds Both bodies will meet after A 6 s C 10 s B 8 s D 12 s

a circle of radius r due to their mutual gravitational Two particles of equal mass m are moving round interaction The speed of each particle will be 1 2 3 GM with GM V 4r

3 At what height from the surface of earth the gravitation potential and the value of g are 5 4 x 107 J kg and 6 0 m s 2 respectively Take the radius of earth as 6400 km a 1400 km c 2600 km b 2000 km d 1600 km NEET I 2016

S The ratio of energy required to raise a satellite to a height h above the earth surface to that required to put it into the orbit is a h 2R b 2h R hody of supercondense c R h d h R material with mass twice ll compared to the

V 3g 8 Let E be the energy required to raise a satellite to height h above earth s surface and E be the energy required to put the same satellite into orbit at that height Then E E is equal to b a c 2h R 2h R R h 1090 2h 2R 3h 20 2R 2h R d earth with orbital which

0 Calculate the force of gravity between a 3 kg newborn baby and a 75 kg doctor standing 1 m away 1 3 5 x 10 7 N 2 6 x 104 N 3 2 x 10 6 N 4 1 5 10 N

1 An astronaut accidentally gets separated out of his small spaceship accelerating in interstellar space at a constant rate of 100 m s2 What is the acceleration of the astronaut at the instant after he is separated from the spaceship Neglect effect of gravitation of nearby stars etc a 100 m s opposite to direction of motion of spaceship b 100 m s2 along the motion of spaceship c Zero d 50 m s in any random direction

Two particles of mass m and M are initially at rest at infinite distance Find their relative velocity of approach due to gravitational attraction when d is their separation at any instant 2G M m d G M m 2d a V c b G M m V d d G M m 4d tonsig OR fonergy required to raise a satellite to a to that required to

from the centre of a uniform sphere of 54 The magi 12 and 71 radius R and mass M are F and F2 respectively Then more than one are correct F if R and r R 12 a b c F2 F F2 2 i if 2 12 F2 12 R and 2 R F 2 if R and r R 1 F2 if R and r R al force at distances moita

1 sketch a graph that shows the proper relationship Case A Gravitational Potential Energy Eg Total gravitational potential energy is zero at infinity Gravitational potential energy is negative Maximum value is zero

Calculate the minimum velocity which should be provided at lowermost point w r t cabin so that particle can just complete the circle 1 zgl 2 Cabin moving upward with acceleration g 2 A g D New Lig

3 A Gravitational potential is constant everywhere inside a spherical shell R Gravitational field inside a spherical shell is zero everywhere

A Field created by the point mass in its surroundings is a non uniform gravitational field and it is dependent R Since the field is E GM r on r hence Non uniform

A If the force of gravitation is inversely proportional to the distance r rather than 2 given by Newton then orbital velocity of the satellite around the earth is independent of r R GMm mv r so v GM

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude which of the following is not correct 1 Raindrops will fall faster 2 Walking on the ground would become more difficult 3 g on the Earth will not change 4 Time period of a simple pendulum on the Earth would decrease

A cavity of the 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 sphere and cavity is opposite to the centre of the cavity Here g where M is the mass of the sphere GM R A mg 2 B 3 mg 8 Correct Answer mg 16

4 A voltmeter with resistance 500 2 is used to measure the emf of a cell of internal resistance 49 The percentage error voltmeter will be nearly in the reading of the 1 0 2 3 1 4 2 0 8 4 2 2 CEN

15 Two satellites of mass m and 2 m are revolving in two circular orbits of radii r and 2r around an imaginary planet on the surface of with gravitational force is inversely proportional to distance from its centre The ratio of orbital speed of satellites is 1 1 1 2 1 2 3 2 1 4 1 5

3GM r 3 D If gravitational field intensity is E at distance R 2 outside from then surface of a thin shell of radius R the gravitational field intensity at distance R 2 from its centre is 1 Zero 3 2E 4 6GM 5r 2 2E 3E

XGM If the energy required to dissemble particles of earth upto infinite distance is Where M Mass of earth R Radius of earth Evaluate x 3 E U U E 0 3 GM 3 GM 5 R 5 R 5R ID

Reliable INSTITUTE JEE MAIN MARCH 2021 DATE 16 03 2021 SHIFT I Unleashing Potential A planet is revolving around sun in elliptical orbit Maximum minimum distance of planet from sun are respectively 1 6 10 2 m and 6 100 m Find minimum speed if maximum speed of planet is 8 10 m s 1 3 x 10 m s 2 3 x 10 m s 3 ns 3 ol L m Vmax Imin m Vmin Imax 8 10 6 10 0 Vmin 1 6 10 2 X X 3 8 x 10 m s 4 4 x 10 m s

If you weigh 655 N on the earth what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 19 0 km Take the mass of the sun to be m 1 99x1030 kg the gravitational constant to be G 6 67 10 11 Nm kg2 and the free fall acceleration at the earth s surface to be g 9 8 m s Express your weight War in newtons View Available Hint s Wstar VAE 1 2210 4 Patty N

The 11 A large number of identical point masses m are placed along x axis at x 0 1 2 4 magnitude of gravitational force on mass at origin x 0 will be Y mm m x 0 x 1 x 2 1 Gm 3 2 Gm m x 4 and so on 2 Gm 5Gm E

Figure shows the elliptical path of a planet about the sun The two shaded parts have equal area If t and t are the time taken by the planet to go from a to b and from c to d respectively then C S b a

ad maximum distances of a planet sun are r and R If the minimum n its trajectory is vo its maximum 2 R m moves around the sun of mass Orbit The maximum and minimum planet from the sun are r and 2 e time period of the planet is say 10 Two point masses m and 4m are separated by a distance d on a line A third point mass m is to be placed at a point on the line such that the net gravitational force on it is zero d m 4m The distance of that point from the m mass is 1 W QN O D4 D5