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A point $P (R \sqrt{3}, 0, 0)$ lies on the axis of a ring of mass $M$ and radius $R$ . The ring is located in $y - z$ plane with its centre at origin $O$ . A small particle of mass $m$ starts from $P$ and reaches $O$ under gravitational attraction only. Its speed at $O$ will be

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Important Questions on Gravitation

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 9

Two spherical bodies of masses $m$ and $5 m$ and radii $R$ and $2 R$ respectively are released in free space with initial separation between their centres equal to $12 R$ . If they attract each other due to gravitational force only, then the distance covered by smaller sphere just before collision will be

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 10

The energy of a satellite in a circular orbit is

E_{0}

. The energy required to move the satellite to a circular orbit of

3

times the radius of the initial orbit is

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 11

Two identical thin rings each of radius

R

are coaxially placed at a distance

R

. If the rings have a uniform mass distribution and each has mass

m_{1}

and

m_{2}

respectively, then the work done in moving a mass

m

from centre of one ring to that of the other is

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 12

A person brings a mass of

1 kg

from infinity to a point

A

. Initially, the mass was at rest but it moves at a speed of

2 m s^{- 1}

as it reached

A

. The work done by the person on the mass is

- 3 J

. The potential at

A

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 13

A satellite is moving in a circular orbit around the earth with a diameter of orbit

2 R

. At a certain point, a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially. The resulting orbit of the satellite would be

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 14

A particle would take a time

t

to move down a straight tube from the surface of the earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be

t'

. The ratio of

\frac{t}{t'}

will be

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 15

Two particles of mass

m

and

M

are initially at rest at infinite distance. Find their relative velocity of approach due to gravitational attraction, when

d

is their separation at any instant

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Complete Study Pack for Engineering Entrances Objective Physics Vol 1>Chapter 10 - Gravitation>Objective Problems>Q 16

An earth satellite of mass

m

revolves in a circular orbit at a height

h

from the surface of the earth.

R

is the radius of the earth and

g

is the acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

A point PR3,0,0 lies on the axis of a ring of mass M and radius R. The ring is located in y-z plane with its centre at origin O. A small particle of mass m starts from P and reaches O under gravitational attraction only. Its speed at O will be

Important Questions on Gravitation

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A point $P (R \sqrt{3}, 0, 0)$ lies on the axis of a ring of mass $M$ and radius $R$ . The ring is located in $y - z$ plane with its centre at origin $O$ . A small particle of mass $m$ starts from $P$ and reaches $O$ under gravitational attraction only. Its speed at $O$ will be