EASY

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Consider a planet moving in an elliptical orbit around the Sun. The work done on the planet by the gravitational force of the Sun:

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Important Questions on Gravitation

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

If the gravitational field in the space is given as

(- \frac{K}{r^{2}})

. Taking the reference point to be at

r = 2 cm

with gravitational potential

V = 10 J {kg}^{- 1}

. Find the gravitational potentials at

r = 3 cm

in SI unit (Given, that

K = 6 J cm {kg}^{- 1}

)

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two objects of masses

4 \times 10^{36} kg

and

9 \times 10^{36} kg

are placed

10^{10} m

apart. The gravitational potential at the point of zero gravitational field, created by these objects is________

[G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}]

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A particle of mass

m

is rotating in a circular orbit of radius

r

under the action of gravity in the presence of another stationary particle of very large mass

M (M ≫ m)

. Consider that the gravitational potential energy is zero at infinite separation. If the total energy of the rotating particle is

E

then, which the following expression correctly represent the angular momentum of the particle?

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A satellite is moving with a constant speed

v

in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

On the

x

-axis and at a distance

x

from the origin, the gravitational field due to a mass distribution is given by

\frac{a x}{{(x^{2} + a^{2})}^{3 / 2}}

in the

x

-direction. The magnitude of the gravitational potential on the

x

-axis at a distance

x

, taking its value to be zero at infinity is:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The ratio of escape velocity at earth

(v_{e})

to the escape velocity at a planet

(v_{p})

whose radius and mean density are twice as that of earth is:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two bodies of masses

m

and

4 m

are placed at a distance

r

. The gravitational potential at a point on the line joining them, where the gravitational field is zero, is

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth

(m a s s = 5.98 \times 10^{24} k g)

have to be compressed to be a black hole?

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A particle of mass

M

is situated at the centre of a spherical shell of same mass and radius

a

. The magnitude of the gravitational potential at a point situated at

\frac{a}{2}

distance from the centre, will be

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two bodies of masses

m

and

4 m

are placed at a distance

r

. The gravitational potential at a point on the line joining them where the gravitational field is zero is

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two bodies, each of mass

M

, are kept fixed with a separation of

2 L

. A particle of mass

m

is projected from the midpoint of the line joining their centers, perpendicular to the line. The gravitational constant is

G

. The correct statement (s) is (are) :

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two particles of identical mass are moving in circular orbits under a potential given by

V (r) = K r^{- n}

, where

K

is a constant. If the radii of their orbits are

r_{1}, r_{2}

and their speeds are

v_{1}, v_{2}

respectively, then

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is

3 \times 10^{5}

times heavier than the Earth and is at a distance

2.5 \times 10^{4}

times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is

v_{e} = 11.2 km s^{- 1}

. The minimum initial velocity

(v_{s})

required for the rocket to be able to leave the Sun-Earth system is closest to

(Ignore the rotation and revolution of the Earth and the presence of any other planet)

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two bodies of mass

m

and

9 m

are placed at a distance

R

. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (

G =

gravitational constant):

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A rocket has to be launched from earth in such a way that it never returns. If

E

is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have, if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is

64

times the volume of the moon.

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A satellite of mass

M

is launched vertically upwards with an initial speed

u

from the surface of the earth. After it reaches height

R

(

R =

radius of the earth), it ejects a rocket of mass

\frac{M}{10}

so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (

G

is the gravitational constant;

M_{e}

is the mass of the earth):

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A uniform cable of mass

M

and length

L

is placed on a horizontal surface such that its

{(\frac{1}{n})}^{t h}

part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

In some region, the gravitational field is zero. The gravitational potential in this region

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The gravitational field in a region is given by

\vec{g} = (5 \hat{i} + 12 \hat{j}) N {kg}^{- 1}

. The change in the gravitational potential energy of a particle of mass

2 kg

when it is taken from the origin to a point

(7 m, - 3 m)

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $(\frac{R}{2})$ is removed as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the centre of the cavity thus formed is ( $G =$ gravitational constant)

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Consider a planet moving in an elliptical orbit around the Sun. The work done on the planet by the gravitational force of the Sun:

Important Questions on Gravitation

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