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Revision Quiz on Gravitation

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Question 1

Four particles each of mass M, are orbiting in a circle of radius R in the same sense of rotation due to their mutual gravitational force of attraction. The time period of revolution is

Question 2

A lighter planet revolving around a very massive star in a circular orbit of a radius R with a period of revolution T. If the Attraction of gravitational force between the planet and the star is proportional to

then

is proportional to

Question 3

A vertical tunnel is dug up through Earth passing through the center as shown in the figure.

A particle of mass m is thrown inside the tunnel. How will the density vary with radius R inside the earth if the particle executes perfect simple harmonic motion?

Question 4

The time period of the moon of the earth is 24 hours. If the separation between the earth and the moon is decreased to 10 times the previous value, the new time period will become

Question 5

If the mean distance of Venus from the sun is

times the distance of earth from the sun and that of the mean distance of Jupiter is 4 times the distance of the earth from the sun, then the ratio of the time periods of Venus and Jupiter will be

Question 6

If the distance of the Earth from the Sun is 1.6 X 10¹¹ m and a comet completes the revolution around the Sun in 678 days then what will be its average distance from the Sun?

Question 7

Two hypothetical planets of masses m₁ and m₂ are at rest when they are at the infinite distance from each other. Because of the gravitational force, they move towards each other along the line joining their centers. What is their speed when their separation is d?
(Speed of m₁ is

and that of m₂ is

)

Question 8

The gravitational field in a region is given by

. The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point (7m, - 3m) is:

Question 9

In an empty universe, there are only two planets A and B, whose mass are 500 kg and 2000 kg, respectively. Both planets are 300 km apart. Find the gravitational potential from planet A at a point on the line joining the both, where the gravitational field is zero.

Question 10

A particle is projected upwards from the surface of the earth with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise:

Question 11

A particle of mass m is projected upwards with velocity

where V_e is escape velocity. At highest point the potential energy of the particle is –

Question 12

The escape velocity for the earth is v_e. The escape velocity for a planet whose redius is

th of the radius of the earth and mass half that of the earth is

Question 13

Jim Carry launched a sphere that looks like a ball from the top of Nanga Parbat. The sphere moves in circular orbit around the earth, at the height of Nanga Parbat, which is 9000m. Acceleration due to gravity near the earth's surface is g. The magnitude of the sphere's acceleration while in orbit is

Question 14

If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh

. Radius of the Earth is 6400 km and

Question 15

The mass density of a spherical body is given by

for

and

for

, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is:

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Aug 25JEE & BITSAT