JEE Physics Gravitation MCQs Set B

Question: If L is the angular momentum of a satellite revolving around earth in a circular orbit of radius r with speed v, then

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The orbital speed of a satellite revolving around a planet in a circular orbit is v₀. If its speed is increased by 10%, then

• a) It will start rotating in an elliptical orbit
• b) It will escape from its orbit
• c) It will continue to move in the same orbit
• d) It will move in a circular orbit of radius 20% more then radius of initial orbit

Answer: It will start rotating in an elliptical orbit

Question: The magnitude of potential energy per unit mass of an object at the surface of earth is E, then the escape velocity of the object is

• a)

  

• b)

  

• c)

  

• d)

  2E

Answer:

Question: The particles A and B of mass m each are separated by a distance r. Another particle C of mass M is placed at the midpoint of A and B. Find the work done in taking C to a point equidistant r from A and B without acceleration (G = Gravitational constant and only gravitational interaction between A, B and C is considered)

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: 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 which gravitational force is inversely proportional to distance from its centre. The ratio of orbital speed of satellites is

• a) 1 : 1
• b) 1 : 2
• c) 2 : 1
• d)

  

Answer: 1 : 1

Question:  A satellite of mass m is revolving close to surface of a planet of density d with time period T. The value of universal gravitational constant on planet is given by

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: When energy of a satellite-planet system is positive then satellite will

• a) When energy of a satellite-planet system is positive then satellite will
• b) Escape out with minimum speed
• c) Move around planet in elliptical orbit
• d) Move around planet in circular orbit

Answer: When energy of a satellite-planet system is positive then satellite will

Question: If radius of an orbiting satellite is decreased, then its kinetic energy

• a) Increases and potential energy decreases
• b) And potential energy increase
• c) And potential energy decrease
• d) Decreases and potential energy increases

Answer: Increases and potential energy decreases

Question: Two point masses having m and 4m are placed at distance at r. The gravitational potential at a point, where gravitational field intensity zero is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: 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

• a) Zero
• b) 2 E
• c)

  

• d)

  

Answer: Zero

Question: Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

• a) –4G
• b) –G
• c)

  

• d)

  

Answer: –4G

Question: If potential at the surface of earth is assigned zero value, then potential at centre of earth will be (Mass = M, Radius = R)

• a)

  

• b)

  

• c)

  

• d) 0

Answer:

Question:

• a) Start rotating around earth in a circular orbit
• b) Escape from gravitational field of earth
• c) Fall back on surface of earth by following hyperbolic path
• d) Fall back on surface of earth by following parabolic path

Answer: Start rotating around earth in a circular orbit

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If potential energy of a body of mass m on the surface of earth is taken as zero then its potential energy at height h above the surface of earth is [R is radius of earth and M is mass of earth]

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A body of mass 'm' taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

• a)

  

• b)

  

• c) 3mgR
• d) mg2R

Answer: 

Question:

• a)

  

• b)

  

• c) 5
• d) 10

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A particle of mass 'm' is kept at rest at a height 3R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: If v_e is escape velocity and v_o is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Which one of the following plots represents the variation of gravitational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R.G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: At what altitude (h) above the earth’s surface would the acceleration due to gravity be one fourth of its value at the earth’s surface?

• a) h = R
• b) h = 4R
• c) h = 2R
• d) h = 16R

Answer: h = R

Question: If the gravitational force between two objects were proportional to 1/R (and not as 1/R²), 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

• a) R⁰ (independent of R)
• b) R
• c)

  

• d)

  

Answer: R⁰ (independent of R)

Question: The distance of two planets from the sun are 10¹³ m and 10¹² m respectively. The ratio of time periods of the planets is

• a)

  

• b)

  

• c) 10 : 1
• d) 1 : 1

Answer:

Question: The radius of earth is about 6400 km and that of Mars is 3200 km. The mass of the earth is about 10 times the mass of Mars. An object weighs 200 N on the surface of Earth. Its weight on the surface of mars will be

• a) 80 N
• b) 40 N
• c) 8 N
• d) 20 N

Answer: 80 N

Question: The earth (mass = 6 × 10²⁴ kg) revolves around the sun with an angular velocity of 2 × 10^–7 rad/s in a circular orbit of radius 1.5 × 10⁸ km. The force exerted by the sun on the earth, in newtons, is

• a) 36 × 10²¹
• b) 27 × 10³⁹
• c) Zero
• d) 18 × 10²⁵

Answer: 36 × 10²¹

Question:  Two particles of equal mass m go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: What will be the formula of mass of the earth in terms of g, R and G?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

• a) 4
• b) 5
• c) 2
• d) 3

Answer: 4

Question: The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth’s mass increases to twice its present value and radius of the earth becomes half, the escape velocity becomes

• a) 22.4 km/s
• b) 44.8 km/s
• c) 5.6 km/s
• d) 11.2 km/s

Answer: 22.4 km/s

Question: The escape velocity of a sphere of mass m from the surface of earth is given by (G = Universal gravitational constant; M = Mass of the earth and R_e= Radius of the earth)

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be

• a) 32 N
• b) 36 N
• c) 144 N
• d) 50 N

Answer:  32 N

Question: A planet has mass equal to mass of the earth but radius one fourth of radius of the earth. Then escape velocity at the surface of this planet will be

• a) 22.4 km/s
• b) 11.2 km/s
• c) 5.6 km/s
• d) 44.8 km/s

Answer: 22.4 km/s

Question: With what velocity should a particle be projected so that it attains a height equal to radius of earth?

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The acceleration due to gravity on a planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B?

• a) 18 m
• b) 2/9 m
• c) 6 m
• d) 2/3 m

Answer: 18 m

Question: Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

• a) F
• b) 3F
• c) F / 3
• d) F / 9

Answer: F

Question: The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, then the radius of the planet would be

• a)

  

• b)

  

• c) 4R
• d) 2R

Answer:

Question: For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

• a)

  

• b)

  

• c)

  

• d) 2

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The escape velocity of a body from this platform is fv, where v is its escape velocity from the surface of the Earth. The value of f is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) S₁ and S₂ are moving with the same speed
• b) The potential energies of earth and satellite in the two cases are equal
• c) The kinetic energies of the two satellites are equal
• d) The time period of S₁ is four times that of S₂

Answer: S₁ and S₂ are moving with the same speed

Question: 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 continue to move with the same speed along the original orbit of spacecraft
• b) It will move with the same speed, tangentially to the spacecraft
• c) It will go very far in the space
• d) It will fall down to the earth gradually

Answer: It will continue to move with the same speed along the original orbit of spacecraft

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R₁ to another of radius R₂(R₂> R₁) is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below

• a) (d)
• b) (a)
• c) (b)
• d) (c)

Answer: (d)

Question:

• a) t₁= 2 ₂
• b) t₁= 4 t₂
• c) t₁ > t₂
• d) None of this

Answer: t₁= 2 ₂

Question: The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be

• a) 6 V
• b) 12 V
• c)

  

• d)

  

Answer: 6 V

Question: If potential at the surface of earth is assigned zero value, then potential at centre of earth will be (Mass = M, Radius = R)

• a)

  

• b)

  

• c) 0
• d) None of these

Answer:

Question: A body of mass 'm' taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

• a)

  

• b)

  

• c) Both
• d) None of these

Answer: