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Two bodies each of mass $M$ are kept fixed with a separation $2 L$ . A particle of mass $m$ is projected from the mid-point of the line joining their centres perpendicular to the line. The gravitational constant is $G$ . The correct statement $(s)$ is (are)

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Important Questions on Gravitation

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two planets have masses

M

and

16 M

and their radii are a and

2 a

, respectively. The separation between the centres of the planets is

10 a

. A body of mass

m

is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

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

The change in potential energy when a body of mass

m

is raised to a height

n R

from the earth's surface is (

R =

radius of earth),

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

If the moon is to escape from the gravitational field of the earth forever, it will require a velocity ___ .

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

A spherically symmetric gravitational system of particles has mass density $ρ = \{\begin{cases} ρ_{0} for r \leq R \\ 0 for r > R \end{cases}$ where, $ρ_{0}$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $v$ as a function of distance $r (0 < r < \infty)$ from the centre of the system is represented by

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Planet

A

has mass

M

and radius

R .

Planet

B

has half the mass and half the radius of Planet

A .

If the escape velocities from the Planets

A

and

B

are

v_{A}

and

v_{B},

respectively, then

\frac{v_{A}}{v_{B}} = \frac{n}{4} .

The value of

n

is:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A space station is at a height equal to the radius of the Earth. If '

V_{E}

' is the escape velocity on the surface of the Earth, the same on the space station is _____

V_{E}

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.

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 body is projected vertically upwards from earth's surface with velocity

2 v_{e},

where

v_{e}

is escape velocity from earth's surface. The velocity when body escapes the gravitational pull is

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:

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

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Escape velocity when a body of mass

m

is thrown vertically from the surface of the earth is

v,

what will be the escape velocity of another body of mass

4 m

is thrown vertically

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A particle falls towards earth from infinity. Its velocity on reaching the earth would be:

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

If a projectile has a velocity greater than the escape velocity, which trajectory will it follow?

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A mass '

m

' on the surface of the Earth is shifted to a target equal to the radius of the Earth. If '

R

' is the radius and '

M

' is the mass of the Earth, then work done in this process is:

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:

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

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:

Two bodies each of mass M are kept fixed with a separation 2L. A particle of mass m is projected from the mid-point of the line joining their centres perpendicular to the line. The gravitational constant is G. The correct statement s is (are)

Important Questions on Gravitation

Learn and Prepare for any exam you want !

Two bodies each of mass $M$ are kept fixed with a separation $2 L$ . A particle of mass $m$ is projected from the mid-point of the line joining their centres perpendicular to the line. The gravitational constant is $G$ . The correct statement $(s)$ is (are)