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Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by

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Important Questions on Gravitation

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 37

The gravitational force exerted by the Sun on the Moon is about twice as great as the gravitational force exerted by the earth on the Moon, but still Moon is not escaping from the gravitational influence of the earth. Mark the option which correctly explains the above system.

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 38

A tunnel has been dug into a solid sphere of non-uniform mass density as shown in the figure. As one moves from $A$ to $B,$ the magnitude of gravitational field intensity

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 39

A projectile is fired vertically upwards from the surface of the earth with a velocity

k v_{e}

, where

v_{e}

is the escape velocity and

k < 1

. If

R

is the radius of the earth, the maximum height to which it will rise measured from the centre of earth will be - (Neglect air resistance)

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 40

The planets with radii

R_{1}

and

R_{2}

, have densities

ρ_{1}, ρ_{2}

respectively and atmospheric pressures are

p_{1}

and

p_{2}

respectively. Therefore, the ratio of masses of their atmospheres, neglecting variation of

g

within the limits of atmosphere is

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 41

Two bodies with masses

M_{1}

and

M_{2}

are initially at rest and a distance

R

apart. Then they move directly towards one another under the influence of their mutual gravitational attraction. What is the ratio of the distances travelled by

M_{1}

to the distance travelled by

M_{2} ?

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 43

Imagine a light planet revolving around a very massive star in a circular orbit of radius

r

with a period of revolution

T .

If the gravitational force of attraction between the planet and the star is proportional to

r^{5 / 2},

then the square of the time period will be proportional to

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 44

The masses and the radii of earth and moon are

M_{1}, R_{1}

and

M_{2}, R_{2}

respectively. Their centres are at distance

d

apart. The minimum speed with which a particle of mass

m

should be projected from a point midway between the two centres to escape to infinity is

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Physics For Joint Entrance Examination JEE (Advanced): Mechanics II>Chapter 5 - Gravitation>Exercises>Q 45

A skylab of mass

m kg

is first launched from the surface of the earth in a circular orbit of radius

2 R

(from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius

3 R .

The minimum energy required to place the lab in the first orbit and to shift the lab from first orbit to the second orbit are

Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by

Important Questions on Gravitation

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Four similar particles of mass $m$ are orbiting in a circle of radius $r$ in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by