CBSE Class 11 Physics Gravitation Solved Examples

Assertion and Reason

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question : Assertion: A body is projected up with a velocity equal to half the escape velocity from the surface of the earth. If R is the radius of the earth and atmospheric resistance is neglected, it will attain a height h = R/3 .
Reason: The gravitational potential is –GM/R on the surface of the earth and it increases with height; M being the mass of the earth.
Answer : A

Question : Assertion: An astronaut inside a massive space-ship orbiting around the earth will experience a finite but small gravitional force.
Reason: The centripetal force necessary to keep the spaceship in orbit around the earth is provided by the gravitational force between the earth and the spaceship.
Answer : A

Question : Assertion: A comet orbits the sun in a highly elliptical orbit. Its potential energy and kinetic energy both change over the orbit but the total energy remains constant throughout the orbit.
Reason: For a comet, only the angular momentum remains constant throughout the orbit.
Answer : B

Question : Assertion: Gravitational potential of earth at every place on it is negative.
Reason: Everybody on earth is bound by the attraction of earth.
Answer : C

Question : Assertion: The total energy (kinetic + potential) of a satellite moving in a circular orbit around the earth is half its potential energy.
Reason: The gravitational force obeys the inverse square law of distance.
Answer : B

Question : Assertion: Two bodies of masses m₁ = m and m₂ = 3m are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach when they are at a separation r is v √2Gm/r
Reason: The gain in the kinetic energy of each body equals the loss in its gravitational potential energy.
Answer : C

Question : Assertion: The binding energy of a satellite does not depended upon the mass of the satellite.
Reason: Binding energy is the negative value of total energy of satellite.
Answer : B

Question : Assertion: For a satellite revolving very near to earth’s surface the time period of revolution is given by 1 hour 24 minutes.
Reason: The period of revolution of a satellite depends only upon its height above the earth’s surface.
Answer : A

Question : Assertion: The speed of revolution of an artificial satellite revolving very near to the earth is 8 km s^–1.
Reason: Orbital velocity of a satellite becomes independent of height of satellite.
Answer : D

Question : Assertion: Earth has an atmosphere but the moon does not.
Reason: Moon is very small in comparison to earth.
Answer : E

Question : Assertion: If take more fuel for a spacecraft to travel form the earth to moon than for the return trip.
Reason: The point of zero gravitational field intensity due to earth or moon is lying nearer to moon i.e., in diagram shown for r < r_0, E_g is towards earth’s center and for r > r_0. E_g is towards moon’s center and at 0 , r = r_0, E_g is zero.

Answer : B

Question : Assertion: Gravitational force between two particles is negligible small compared to the electrical force.
Reason: The electrical force is experienced by changed particles only.
Answer : A

Question : Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will becomes some at all places.
Reason: The value of acceleration due to gravity is independent of rotation of earth.
Answer : A

Question : Assertion: Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution.
Reason: According to Kepler’s third law of planetary motion, square of time period is proportional to cube of mean distance from sun.
Answer : A

Question : Assertion: Two satellites following one another in the same circular orbit. If one satellite tries to catch another (leading) satellite, then it can be done by increasing its speed without changing the orbit.
Reason: The energy of earth-satellite system in circular orbit is given by E = - GMm/2r where r is the radius of the circular orbit.
Answer : C

Comprehension Based

Paragraph –I

Escape velocity is the velocity with which if body is projected will move out of gravitational field of earth never to return back to earth. The escape velocity depends on different factors. To test your knowledge of factors on which escape velocity depends answer the following questions.

Question : Choose the correct statement:
a. Escape velocity is independent of mass of body
b. Escape velocity is directly proportional to mass of body
c. Escape velocity is inversely proportional to mass of body
d. Escape velocity is directly proportional to square root of mass of body
Answer : A

Question : Escape velocity form any planet is proportional to mass of planet M as  υ_e ∝ Mⁿ where n is:
a. 1
b. 1/2
c. 1
d. - 1/2
Answer : B

Question : Escape velocity from any planet depends on size of planet or its radius as υ_e ∝ Rⁿ where n is:
a. - 1/2
b. 1/2
c. 1
d. –1
Answer : C
 

Ex.1 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 move in a circle while maintaining the original mutual separation a. Find the initial velocity that should be given to each particle and also the time period of the circular motion.

Ex.2 Two satellites S1 and S2 revolve round a planet in coplanar circular orbits in the same sense. Their peirods of revolution are 1 hours and 8 hours respectivley. The radius of the orbit of S1 = 104 km. When S2 is closest to S1, find
(a) the speed of S1 relative to S2,
(b) the angular speed of S2 as actually observed by an astronaut in S1.

Ex.3 A pair of stars rotate about their common centre of mass. One of them has mass m and the other 2m. Their centres are a distance d apart, d being large compared to the size of either star.

(a) Derive an expression for the period or rotation of the stars about their common centre of mass in terms of d, m and G.
(b) Compare the angular momenta of the two stars about their common centre of mass.
(c) Compare the kinetic energies of the two stars.

Sol.: The centre of mass O is at a distance 2d/3 from the star of mass m and d/3 from the star of mass 2m. Both the stars rotate with the same angular velocity ω.
(a) Since the gravitational force provides the centripetal force, then