Gravitation Questions and Answers

1 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 Take PG QG RG 1 m Now FGP FGQ FGR 2m PA2m G The angle between GR and the positive x axis is 30 Similarly the angle between GQ and negative x axis is 30 G 2m m 1 m30 G 2m m icos 30 j sin 30 1 G 2m m i cos 30 sin 30 1 R By principle of superposition we get FR FGP FGQ FGR 2m X i e along positive y axis FR 2GM j 2Gm i cos 30 j sin 30 2Gm i cos 30 sin 30 0 ii By symmetry all the x component of the force will cancel out each other FR 8Gm j 2 Gm i sin 30 2Gm i sin 30 8Gm 4Gm sin 30 8Gm j 2Gm j

India s Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun It leaves the earth at E and meets Mars at M If the semi major axis of Earth s orbit is ae 1 5x1011 m that of Mar s orbit am 2 28x 10 m taken Kepler s laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to 1 500 days 2 320 days 4 220 days 3 260 days M am Mars orbit ae Sun E Earth orbit Mars orbit 3

From a sphere of mass M and radius R a smaller sphere of radius R 2 is carved out such that the cavity made in a original sphere is between its centre and the periphery see figure For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R the gravitational force between the two spheres is 1 2 3 41GM 450R 41GM 3600R 4 GM 225R 59GM 450R 3R

Try Yourself 3 The period of revolution of a satellite in an orbit of radius 2R is T What will be its period of revolution in an orbit of radius 8R Hint By Kepler s third law The radius of the nearly circular orbit of mercury is 5 8 x 1010 m and its orbital period is 88 days If a hypothetical planet has an orbital period of 55 days what is the radius of its circular orbit Hint By Kepler s third law SAL LAW OF GRAVITATION orically it was the Italian astronomer and physicist Galileo Galilei 1564 1642 who recognized the all bodies irrespective of their masses are accelerated towards earth with a constant acceleration

9 At what height from the surface of earth the gravitation potential and the value of g are 5 4 x 10 J kg an 6 0 ms respectively Take the radius of earth as 6400 km 1 2600 km 2 1600 km 3 1400 km 4 2000 km

a 67 A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F of the sphere A spherical cavity of radius R 2 is now on a particle placed at a distance 2R from the centre made in the sphere as shown in the figure The sphere with cavity now applies a gravitational force do na st F F on the same particle The ratio F 5ola 9 R R 2 2R b A 7187 2 is dligs 10 tonele A be cove

A satellite with a mass of 100 kg is launched from the earth at an altitude of h 500 km with Vo 1 1 V According The launch status angle is10 degrees to this a Shape of orbit a e period of orbit P b 30 minutes after the launch the satellite s r f

If the gravitational force between two objects were proportional to 1 R and not as 1 R where R is the distance between them then a particle in a circular path under such a force would have its orbital speed v proportional to 1 R 2 3 RO independent of R In t

Let the speed of the planet at the perihelion P in fig given below be vp and the Sun planet distance SP be rp Relate rp Vp to the corresponding quantities at the aphelion rA VA Will the planet take equal times to traverse BAC and CPB School Board NCERT 13 S B O 2a S 2b

The depth at which the effective value of acceleration 2 due to gravity is is R radius of earth 3R 1 R R clev 2 2 Three identical mass M are placed at corner of 13 at det er for 1 R 3 RY f 2 3R 2 SE THE FORMER

Three identical mass M are placed at corner of 3 equilateral triangle of side L then calculate escape velocity given to a mass m placed at centroid at an equilateral triangle 6 2GM 3 6 3GM 3GM 21 3GM Ang TRI NHI T HOT LB TH I nh v t a fun and a fam 1 6 2GM 6 3GM 3GM 2L 3GM

Physics Question Palette Question No 23 A spaceship is launched into a circular orbit close to the earth s surface What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull Radius of earth 6400 km g 9 8 m s Options 3 28

A tunnel is made in earth passing through centre of earth If time taken by an object to move from one end of tunnel to other end depends on radius of earth R and acceleration due to gravity g as T kRgh where k is dimensionless constant find a b

5 A satellite is revolving round the earth with 36 3448 year in f orbital speed v If it is imagined to stop suddenly the speed with which it will strike the surface of the earth would be v escape velocity of a body from earth s surface 1 v v 3 2 2 Vo 4 2 2 far as standa frent staten and found as year oft ude 4 1 v vo 3 2 2 Vo 4 2 2

An artificial satellite orbiting around the Earth does not fall down This is so because the attraction of Earth A does not exist at such distance B is neutralised by the attraction of the Moon C provides the necessary speed for its steady motion D provides the necessary acceleration for its motion

The value of g at a particular point is 9 8 ms 2 Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass The value of g at the same point assuming that the distance of the point from the centre of earth does not shrink will now be A 4 9 ms 2 B 3 1 ms C 9 8 ms 2 D 19 6 ms

The gravitational potential at height h above the 22 earth s surface is 5 12 x 107 J kg and acceleration due to gravity at this point is 6 4 ms If radius of the earth is 6400 km the value of h is 1 1200 km 3 1800 km 2 1600 km 4 2400 km at han kag u gee u fav 5 12 x 107 J kg 6400 1 1200 km 3 1800 km 6 4 ms 1 afegeft 2 1600 km 4 2400 km

The escape velocity on a planet with radius 35 double that of earth and mean density equal to that of earth will be escape velocity on earth 11 2 km sec 1 11 2 km sec 2 22 4 km sec 3 5 5 km sec 4 15 5 km sec 11 2 km sec 1 11 2 km sec 2 22 4 km sec geat for at ar UN a 3 5 5 km sec 4 15 5 km sec

A 26 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute The base of the ladder is sliding away from the wall At what rate is the ladder sliding away from the wall when the base of the ladder is 10 feet from the wall Would you expect the same rate when the ladder is any distance from the wall Would you expect your answer to be positive when the base is any distance from the wall Is there a physical reason why the rate is positive At what rate is the ladder moving away from the wall when the ladder hits the ground

Q 1 The mass density of a spherical galaxy varies K over a large distance r from its center as Y In that region a small star is in a circular orbit of radius R Then the period of revolution T depends on R as 1 1 T oc 3 TR R 2 T OC R 4 T x R

3 32 7 14 A projectile is fired from the surface of earth wit a velocity Kv K 1 where ve is the escap velocity from surface of earth The maximul height up to which the projectile will rise from th centre of earth will be 1 KR 5 2 K 1 R 4 R R 1 K K 1 15 An elastic metal rod will change its length when 3

A body is suspended from a spring balance kept in a satellite The reading of the balance is W when the satellite goes in an orbit of radius R and is W when it goes in an orbit of radius 2R Mark incorrect options Question Type Multiple Correct Type 1 2 3 W W W W2 W W

Online Mock Test Series for NEET 2020 30 Three mole of an ideal gas is taken through the process ABC as shown in the figure The total work done by the gas is T 27 To P 1 2 RT In2 3 12 RTD In2 E 3 B 31 A particle of mass 10 g is executing SHM according to the equation y 4 sin 4t 1 3 having time period T Kinetic energy of the particle at t T 4 will be 1 9 6 unit 3 1 92 unit 32 A uniform ladder of mass m 40 kg rests against a smooth vertical wall making an angle 30 with horizontal The lower end of ladder rests on a 2P 112 114 8P 2 4 RT In2 4 4 RT In2 rough floor having An electrician having mass 80 kg attempt to climb the ladder to repair house wiring Fraction of length than can be encountered by the electrician before the ladder begins to slip will be 2 0 48 unit 4 0 96 unit 2 1 33 The equation for a wave travelling in x direction on a stretched string is given by y 5 cm sin 2x cm x 100 s f Acceleration of a particle at x 8 cm and t 0 11 s will be 1 1 20 cm s 2 10x cm s 4 Zero 3 5x cm s 34 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 R respectively then which of the following option is correct GMm GMm R r 2 3 mo r E 413 respectively then will be 4 1 3 4 35 An organ pipe X open at one end vibrating in its first overtone is in resonance with another organ pipe Y open at both end vibrating in its third overtone These pipes have lengths and 12 Medica IT IR Mo R 1 10 m s 3 2 5 m s 2 ations GMm R 4 Test 13 Code A me R GMm rR N 318 516 36 The potential energy of a particle having mass 1 kg is given by U 4x 3y Joule where x and y are in metre If the particle was at rest at 16 6 at time t 0 then speed of the particle when it crosses x axis will be me r 2 5 m s 4 15 m s 37 Electromagnetic wave of intensity 1800 W m falls on a completely absorbing spherical surface having radius R as shown in the figure R 3 cm Force exerted by beam on the sphere is 1 108 10 10 N 2 54 x x 10 10 N 3 216 10 10 N 4 Zero 38 Three waves of equal frequency having amplitudes 12 4 and 8 unit meet at a point with successive phase difference of Amplitude of resulting wave will be 1 24 unit 2 12 2 unit 4 20 unit 3 4 2 unit 39 The rate of emission of heat by a black body at temperature T is Q Rate of emission of heat by another body having emissivity half unit and same surface area at temperature 3T is 1 81 Q 3 33 5 Q 2 9 Q 4 40 5 Q

spring at equilibrium near earth surface is xo then the extension in spring at a height 1600 km from earth surface is radius of earth R 6400 km 5x 1 X 16 25 3 2 4

Test 13 Code A 6 The magnitude of uniform magnetic field in a small region of Helmholtz coils is nearly N is number of turns in each coil 2 HONI R 4 0 72 NI R 7 Equivalent capacitance between points A and B as shown in the following circuit will be 2C 2C 8 9 3 HONI 2R 2 NI R 3 2C 2C 1 1 m s 3 2 m s 1 C 3 3C Two small blocks each of mass 2 kg are connected by an inextensible string light Blocks are placed over a fixed smooth wedge as shown in the figure and system is released from rest Magnitude of acceleration of both the blocks will be g 10 m s 37 2 20 4 4C 90 A C X O 53 2 2 m s R B A charged particle Q is placed outside a hollow cone on the axis of a cone at a distance x from the centre of its base Electric flux linked with the slant surface of the cone due to the charge is Aa R 3 Medica 1 Zero 3 Q 4 Online Mock Test Series for NEET 2020 Q 250 E 10 A point charge Q is placed off centre inside a thin conducting shell of radius R as shown in the figure K 0 K 4 3 1 KQ 9R 25R Electric field at point P in this situation will be KQ KQ 1 25R 9R 1 Hol 41 31 50m 31 41 50 3 4 Data insufficient 11 A long straight thin wire is placed along z axis Wire carry a current along negative z direction Magnetic field at any point P having coordinates 3 4 0 is given by Hol 3 4i 25x 2 H 37 41 50 3R 2 P type 5R 4 12 Pure Si at 500 K has equal number of electron n and hole nn concentration of 1 7 x 10 5 m On doping with boron hole concentration n increases to 4 7 x 102 m The doped semiconductor is of 1 N type 2 with electron no 3 5 x 1012 m ne 6 14 x 10 m 3 with electron 3 N type with electron ne 8 2 x 10 m 4 P type with electron ne 2 89 x 10 0 ma concentration concentration concentration concentration

Halley s comet moves in an elliptical orbit about the Sun no external torque act on the system At the furthest point aphelion the comet is a distance r 5 3 10 2 m away from the Sun and its speed at that point is v 913 ms The orbit has its closest approach to the Sun perihelion at r2 8 8 x 10 0 m What is the highest speed the comet will attain in its orbit

The distance between to stars of masses M and 16M is 10a Their radii a and 2a respectively A body of mass m is fired stright from the surface of larger star towards the smaller star If the speed of projection to reach the surface of smaller star is x yGM 2 V a then find the value of x y 8

Inside a uniform sphere of mass M and radius R a cavity of radius R 3 is made in the sphere as shown R B R 3 C A Gravitational field inside the cavity is uniform B Gravitational field inside the cavity is non uniform C The escape velocity of a particle projected from point A is 88GM 45R D Escape velocity is defined for earth and particle system only

the time period of oscillation of a simple pendulum is T 2n VL Vg measured valu of length is 200 CM known to have 1 mm accuracy and time for hundred oscillation is found to be 90 second using a wrist watch of 1 s resolution find the accuracy in determining g 6 54 PM

Three particles each of mass m are situated at the vertices of an equilateral triangle of side a The only forces acting on the particles are their mutual gravitational forces It is desired that each particle moves in a circle while maintaining their original separation a The initial velocity that should be given to each particle is A B C D 3GM V a GM a GM V2a GM 3a

ss than similar same uration Test 7 Code A 22 A planet has twice the density of the earth but the acceleration due to gravity on its surface is same as that on the surface of the earth If R is radius of the earth then that of the planet is 1 R R R4 2 KNRB 8

SolveLancer Test A planet X is made up of material which makes its density times that of earth But the volume of planet is 8 times that of earth The acceleration due to gravity on earth is g Then acceleration due to gravity on planet X is SolveLancer Test a

A student uses a simple pendulum of exactly 1 m length to determine g the acceleration due to gravity He uses a stopwatch with the least count of 1 second for this and records 40 seconds for 20 oscillations For this observation which of the following statements is true A Error A T in measuring T the time period is 0 05 seconds B Error A T in measuring T the time period is 1 second C Percentage error in the determination of g is 5 D Both a and

3 A body is projected from surface of earth with a velocity 2V where V is the escape velocity The velocity of object when it escapes from gravitational field of earth is 1 2V 3 TV 2 3V 4 11V

Distance between the centres of two rings is a The masses of these rings are M and 4M A body of mass m is fired straight from the centre of the heavier ring What should be its minimum initial speed to cross the centre of lighter ring The radius of the both ring is R Assume a R 4 M R a

If in a system the force of attraction between two point masses of 1 kg each situated 1 km apart is taken as a unit of force and is called notwen newton written in reverse order if G 6 67 10 N m kg 2 in SI units then which of the following is true A 1 notwen 6 67 10 newton B 1 newton 6 67 x 10 7 notwen C 1 notwen 6 67 10 17 newton D 1 newton 6 67 x 10 2 notwen

Q 16 A body moving radially away 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 the planet What will be a then velocity in circular orbits b maximum distance between the two fragments before collision and c magnitude of their relative velocity just before they collide

from one end Also find the force of their A remote sensing satellite is revolving in an orbit of radius x on the equator of Earth Find the area on Earth surface in which satellite can not send message

Consider two satellites A and B of equal mass m moving in the same circular orbit of radius r around the Earth E but in opposite sense of rotation and therefore on a collision course see figure i In terms of G M m and r find the total mechanical energy EA Eg of the two satellite plus Earth system before collision ii If the collision is completely inelastic so that wreckage remains as one piece of tangled material mass 2m find the total mechanical energy immediately after collision iii Describe the subsequent motion of the wreckage A M B

A satellite which is geostationary in a particular orbit is taken to another orbit Its distance from the centre of earth in the new orbit is 2 times that of earlier orbit The time period in the second orbit is 1 48 2 hr 2 48 hr 3 24 2 hr 4 24 hr

4 The ratio of the radil of the planets X and Y is a The ratio of acceleration due to gravity is B The ratio of the escape velocities from their surfaces will be 1 o 3 2 a 4 R 5 A uniform conductor of resistance R is cut into 20

At a point A on the earth s surface the angle of dip 8 25 At a point B on the earth s surface the angle of dip 8 25 We can interpret that NEET 2019 1 A and B are both located in the northern hemisphere 2 A is located in the southern hemisphere and B is located in the northern hemisphere 3 A is located in the northern hemisphere and B is located in the southern hemisphere 4 A and B are both located in the southern

In a meter bridge the wire of length 1 m has a non uniform cross section such that the variation dR dR di dl Two equal resistances are connected as shown in the figure The galvanometer has zero deflection when the jockey is at point P What is the length AP JEE Main 2019 of its resistance R with length is A 1 0 2 m R ww R www 1 1 1 2 0 35 m B 1 Ji

A From to A body on earth s surface is at a latitude of 60 N Consider only rotation of earth about its own axis then Take Earth s radius 6400 km A Centripetal acceleration of body is 0 017 m s B Centripetal acceleration of body is 0 034 m s C Centripetal acceleration of body is 1 m s D Centripetal acceleration of body is 9 8 m s

The value of acceleration due to gravity at a point P inside the earth and at another point Q outside the earth is g 2 g being acceleration due to gravity at the surface of earth Maximum possible distance in terms of radius of earth R between P and Q is A 2R B 2R 2 1 R D 2 2 1 2 R C 2 2 1

For a particle in uniform circular motion with speed v in anticlockwise direction as observed from positive z axis the acceleration a at a point R e on the circle of radius Ris Here 0 is measured from the ve x axis in anticlockwise sense 1 2 3 sl sle se sle cosei sinej R V cosej cost sinei R R V 4 cose sinej V R

3 12V mi 4 12V mi 4 Consider a satellite going around the earth in a circular orbit at a height of 2R from the surface of earth where R is the radius of the earth What is the speed of the satellite g acceleration due to gravity at the surface of earth 2 1 3 gR 3 gR 2 112 4 gR 3 2

In 1994 the performer Rod Stewart drew over 3 million people to a concert in Rio de Janeiro Brazil If the people in the group had an average mass of 80 0 kg what collective gravitational force F would the group have on a 4 50 kg eagle soaring 5 00 10 m above the throng Treat the group as a point object What is the ratio R of the force F to the force between Earth and the eagle F R 1 2 x10 6 Incorrect 2 7 X10 8

4 An earth s satellite is revolving in circular orbit in equatorial plane It is used for communication purpose The satellite can transmit signals upto 60 latitude on earth The angular velocity of satellite is 3 GM 2R GM 8R 3GM 4R 3GM 8R3 Minn

3 A satellite is revolving round the earth in circular or with speed v An object of mass m is ejected fro the satellite such that the object just escapes fro earth s gravitational field At the time of ejectic kinetic energy of the object was 1 2 m 3 2m Inoormat 4 mv ction