Gravitation Questions and Answers

3 1 An astronaut with space suit has a mass of 110 kg Climbing up a hill 7 3 m high in 7 2 sec requires the astronaut to expend a power of 200 W Is the astronaut on the earth Ans No

Due to huge cosmic explosion on the sun the earth shrinks and loses 60 of its radius R keeping the mass of the earth unchanged The new value of acceleration due to gravity is a b c d 19 6 m s 61 31 m s 9 81 m s 3921 m s

2 6 Answer A a satellite of mass m is projected from the surface of a stationary spherical planet of mass M m and radius R with a speed equal to escape velocity in radial direction At a height h 2R from the surface of planet a rocket of mass m 4 is projected from the satellite with a speed v and at an angle with the radius vector as a result the satellite starts orbiting around the planet in a circular orbit The choose the correct option s B GM v 5 3R V 41GM 3R Rate this question

58 The gravitational field due to a system concentric thin spherical shells of mass m and m2 and radii and r r2 at the point P Gm 1 m r P be G m m me 3 2 M 1 2 Gm 2 1 4 4 Zero

4 fly upwards with acceleration With what minimum acceleration can a fireman slide down a rope whose breaking strength is th of his weight g gravitational acceleration 1 1 g 2 0 4 g 3 0 6 g 4 0 8 g Three masses of 1 kg 6 kg and 3 kg are

69 Select the angular speed of a geostationary satellite 1 zero 2 rad sec S 73 1800 rad sec 4 Can t be determined 43200 70 A satellite of mass m is revolving in a circular orbit of radius r around a planet of mass M If PE of the orbit is assumed to be zero then its total energy will be 1 33 GMm GMm 2 GMm 2r 4 None of these

56 The force of interaction between the semicircular ring and the particle placed at it centre when each is of mass M is 1 GM R 4GM M R M 2 GM 2 R 2GM

A particle of mass m is taken to height equal to double the radius of earth The increase in Potential Energy of system is g is the acceleration due to gravity at surface 1 mg2R mgR 2 vorle al piw L 3 2mgR 3 112

50 The gravitational field due to mass distribution A in x direction Here A is constant Taking is E 2 X x the gravitational potential to be zero at infinity potential at x is 1 2A X 2 M 2A x A 2x X 1 A missile is launched with velocity less than the

Isolated uniform hollow sphere of mass M and radius R has a point mass m placed at its centre as shown in figure Find out the work done in moving the point mass from the centre to a point A 1 Gm M R m O A M R 2 2 2 Gm M R

2 6 The earth s radius is R and acceleration due to gravity at its surface is g If a body of mass m is sent to a height of R 4 from the earth s surface the potential energy changes by R R 3 4 R 5 1 mg 3 mg 2 mg 4 3 mg R 16

4 Zero A plumb line is suspended from a ceiling of a car moving with a horizontal acceleration of 10 m s The angle of inclination of plumb line with the vertical is g 10 m s 1 60 2 45 3 30 4 90

A satellite is moving on a circular orbit around a planet A sharp impulse is given to the satellite such that it escapes from the gravitational field of the planet The impulse can be given in two different ways as shown The ratio of the impulse given in the two different cases Pis P P2 A 2 B 2 oo C 2 1 P D 2 1

Acceleration due to gravity on the surface of earth is g Acceleration due to gravity on the surface o another planet of same density but radius half tha of earth is 1 2 g 2 Q 2 2 g 4 g

If the gravitational field in a certain region of space is zero then the potential difference between any two points in this region is zero B 2 the potential of every point in the region is zero work required to be done by external agent to move a mass from one point to another is positive but by field is negative 4 All of these

3 3v 1 The 1 Let the minimum external work done in shifting a particle from centre of earth to earth s surface be w and that from surface of earth to infinity be w2 w w is equal to 1 1 1 2 1 2 3 2 1 4 1 3

A planet is revolving around the sun as shown in elliptical path The correct option is B LIBY A S C The time taken in travelling DAB is less than that for BCD 2 The time taken in travelling DAB is greater than that for BCD The linear momentum of planet in travelling DAB remains constant 4 The time taken in travelling CDA is greater than that for ABC

18 A body has been thrown with a speed v from the surface of the earth which is double the escape speed v from the surface of the earth The speed left with the body in interstellar space at infinity will be 1 Ve 3 3 ve 4 Zvo 30 0

A satellite is moving in a circular orbit of radius round the earth Which of the following statements is incorrect LAT Its angular momentum varies as 2 Its linear momentum varies as X35 Its kinetic energy varies as 4 Its frequency varies as TIR 1 R3 2 1 R 11 476234

A particle bob of mass 1 kg is performing vertical circular motion Then 1 3 4 orrect Answer 4 ur Answer 3 m 1 Power delivered by tension at point 4 is negative Power delivered by tension at point 2 is positive Power delivered by gravitational force at point 3 is zero Power delivered by gravitational force at point 4 is negative

As shown in figure when a spherical cavity centred at O of radius 1 is cut out of a uniform sphere of radius R centred at C the centre of mass of remaining shaded part of sphere is at G i e on the surface of the cavity R can be determined by the equation 1 R R 1 2 R 1 2 R R 1 2 R 1 3 R R 1 2 R 1 4 R R 1 2 R 1

2 A particle of mass m moves under the action of central force whose potential is V r Kmr 0 then 65 09 i For what kinetic energy and angular momentum will the orbit be a circle of radius R about the origin ii Calculate the period of circular motion

4 The radius of newly discovered planet is 3 times 14 that of the earth but having same density If acceleration due to gravity on surface of the earth is g and that on surface of new planet is g then 1 g 2g 3 2 g g 3 g 3g 4 g 27g 2 3 4

2 25 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth If the satellite is stopped in its orbit and allowed to fall freely onto the earth the speed with which it hits the surface km s o 98 ms and R 6400 km

Two spacecraft of masses m and m are flying with their engines off in the gravitational field of a star of mass M that is much larger than masses of the spacecraft Speeds of the spacecraft at great distances from the star are equal to U and respectively After passage around the star when the spacecraft are again at great distances from the star the spacecraft move with speeds u and U perpendicular to their initial directions of motion If during passage around the star the minimum distance of the first spacecraft from the star is r what is the minimum distance of the second spacecraft from the star

Q 5 The distance between the centres of moon and earth is D The mass of earth is 81 times the mass of moon At which point between the earth and moon the gravitational force is zero D 4 x 10 km footly black

Two stationary massive spherical objects each with mass M are separated by a d Describe the position velocity and acceleration a For a particle of mass m at d 2 and is allowed perturbations along the line of interaction d b For a particle of mass m at d 2 and is allowed perturbations along the line of interaction d c For both the negative and positive mass allowed for perturbations perpendicular to line of interaction d at d 2

A cannon fires a projectile as shown in figure The dashed line shows the trajectory in the absence of gravity and the solid line shows the trajectory in the presence of gravity Particle will be at A B and C at t 1s t 2s and t 3s respectively Find the value of fY y2 Y3 in meters if g 10 ms 14 t 0 B C 1 1s t 2s t 35 X

A space vehicle moving in a circular orbit of radius r1 transfer to a larger circular orbit of radius r2 by means of an elliptical path between A and B The transfer is accomplished by a burst of speed AV at A and a second burst of speed AV at B Then match the following R is the radius of the earth g is the acceleration due to gravity on the surface of the earth neglect the spin rotation of the earth Column I Velocity at A in a circular orbit of radius r1 B Velocity at A of elliptical orbit perihelion near point of the transferred orbit A P 9 r Column II 2812 R 1 R 281 1 1 1 C Velocity at B of elliptical orbit aphelion far point of the transferred orbit D Velocity increment at B from elliptical path s g to circular orbit R R g 12 50 1 2r 1

Example 2 The rate of a clock in a spaceship Aakashganga is observed from earth to be 5 13 of the rate of the clocks on earth If both Aakashganga and Suryashakti are moving in the same direction relative to someone on earth then the speed of Aakashganga relative to Suryashakti is

19 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 CBSE AIPMT 2011

A planet is revolving around the sun in an elliptical orbit of eccentricity If t and to are the time taken by 4 t the planet in going along ACB and t in returning along BDA then find t D Sun B 3

A mass m travelling at speed V in a straight line from far away is deflected when it passes near by a black hole of mass M which is at a perpendicular distance R from the original line of flight The distance of closest approach a between the mass and the black hole is given by the relation V 1 a R1 R 14 3 a R1 R 2GM aV2 GM 2aV 1 2 1 2 Mo 2 a R1 4 0 av2 2GM 1 2 1 2 a R 1 2GM

A particle of mass m is projected with velocity from the surface of the earth In list 1 different ranges of the speed of the particle are given in P Q R and S In list II the kinetic energy K gravitational potential energy U and total energy E of the earth particle system are given Each case in list I may correspond to one or more choices given in list II Further the point at infinity is taken as the zero potential energy reference level Take escape velocity VE 11 kms List l P Projected with 5 kms 1 making an angle of 30 with the horizontal Q Dropped into a hole drawn along the diameter of earth R Projected with 9 kms 1 S Projected with 11 kms 1 OP 1 2 3 Q 1 25 R 125S 12 45 OP 1 2 3 Q 1 25 R 125S 124 1 2 3 4 5 List II Total energy E is negative Potential energy Ujis negative Kinetic energy K never become zero Total energy K becomes zero Kinetic energy K may become zer

12 There are three arrangement of three point masses each of mass m In which of the following three arrangements they are arranged in order of increasing magnitude of gravitational force on point mass marked as 1 A D B Y k C 1 C B and A 3 C A and B 2 B C and A 4 A C and B 12 6 B f fare con un gran an fungera aft f A D X O 1 ffe 1 C B and A 3 C A and B 2 B C and A 4 A C and B

A block of negligible dimensions and mass m is rigidly attached at P to a ring of mass 3m and radius r The system is released from rest at 8 90 measured w r t vertical and rolls without sliding If the angular acceleration of hoop just after release is Find the value nr of n P

1 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 AIPMT 20141 1 10 9 m 3 10 2 m 2 10 6 m 4 100 m

A uniform cylindrical rod of mass m and density po is having a point mass m at its bottom end m is just the minimum value of mass so that the complete arrangement is just found to be in stable equilibrium at the position shown in diagram The value of ratio of density of liquid to that of rod under the given condition is

A particle is thrown with escape velocity v from the surface of earth Calculate its velocity at heigh 3 R AIIMS 2012 1 9 25 km s 3 11 2 km s 2 5 6 km s 4 4 3 km s

7 The orbital velocity of an artificial satellite in a circular orbit just above the earth s surface is v The orbital velocity of satellite orbiting at an altitude of half of the radius is AMU 2005 3 1 Vo 2 2 V FRA 2v 3 Vo 4 3 Vo

5 Two solid spherical planets of equal radii R having masses 4M and 9M their centre are separated by a distance 6R A projectile of mass m is sent from the planet of mass 4 M towards the heavier planet What is the distance r of the point from the lighter planet where the gravitational force on the projectile is zero 2 AMU 2007 1 1 4 R 3 1 5 R 2 1 8 R 4 2 4 R

A projectile of mass m is thrown vertically up with an initial velocity v from the surface of earth mass of earth M If it comes to rest at a height h the change in its potential energy is AMU 2004 1 GMmh R R h 2 GMmh2 R R h 3 GMmhR R R h 4 GMm hR R h

AMU 9 Read the following statements S An object shall weigh more at pole than at equator when weighed by using a physical balance S It shall weigh the same at pole and equator when weighed by using a physical balance S It shall weigh the same at pole and equator when weighed by using a spring balance S It shall weigh more at the pole than at equator when weighed using a spring balance Which of the above statements is are correct 1 S and S A 3 S and S3 2 S and S4 4 S and S

Mars has a diameter of approximately 0 5 of that of earth and mass of 0 1 of that of earth The surface gravitational field strength on mars as compared to that on earth is greater by a factor of VITEE 2005 1 0 1 3 2 0 2 0 2 4 0 4

12 A geostationary satellite is orbiting the earth at a height of 6R from the earth s surface R is the earth s radius What is the period of rotation of another satellite at a height of 2 5 R from the earth surface AMU 2002 1 6 2 hours 5 5 2 10 hours

SolveLancer Test 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 c d 2x a b

Solvelancer Test What is the time taken by a planetary body to cover an area of 4 million square km if the time taken by the same planetary body to cover an area of 2 million square km is 48 hours Solvelancer Test a b c d 48 hours 24 hours 72 hours 96 hours

A small satellite is in elliptical orbit around the earth as shown L 2 Earth 1 denotes the magnitude of its angular momentum and K denotes its kinetic energy If 1 and 2 denote two positions of the satellite then a L L K K c L L K K b L L K K d L L K K

2 If the size of the Earth were to shrink diameter decreases overnight without any change in its mass would you get up in the morning and find yourself heavier or lighter or would you still weigh the same Give reasons for your answer mars 200g takes 4s to reach the bottom when dropped from a height c

Figure shows a planet in an elliptical orbit around the sun S Where the kinetic energy of the planet is maximum P3 1 P 2 P2 Question Type Single Correct Type 3 P P S P P