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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.

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Important Questions on Gravitation

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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

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) :

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

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

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Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The gravity potential energy is maximum at

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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 particle of mass

m

is projected with a velocity

v = k V_{e} (k < 1)

from the surface of the earth (

V_{e} =

escape velocity). The maximum height above the surface reached by the particle is___

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),

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Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

An object of mass

1 kg

is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If,

g = 10 m s^{- 2}

and radius of earth

= 6400 km

]

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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

What is the minimum energy required to launch a satellite of mass

m

from the surface of the earth of mass

M

and radius

R

at an altitude

2 R

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Consider a satellite which is rotating in a circular orbit of radius

2 R_{E}

about the earth. The mass of satellite is

1600 kg .

What is the energy required to transfer it to a circular orbit of radius

8 R_{E} ?

[

use

g = 10 ms s^{- 2}, R_{E} = 6 \times 10^{6} m]

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A planet is orbiting the sun in an elliptical orbit. Let

U

denote the potential energy and

K

denote the kinetic energy of the planet at an arbitrary point on the orbit. Choose the correct statement-

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The gravitational potential energy difference per unit mass between the surface of a planet and a point

100 m

above it is

1000 {Jkg}^{- 1}

. How much work is required to be done in moving an

5 kg

object

100 m

on a slope

30 °

to the horizontal on this planet?

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A rocket is launched vertically from the surface of the earth with an initial velocity equal to one-third of the escape velocity. If we ignore the atmospheric resistance, what will be the maximum height attained by the rocket?

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Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Four spheres each of mass $m$ form a square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is

Question Image

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A body of mass is taken from earth surface to the height

h

equal to twice the radius of earth

(R_{e})

, the increase in potential energy will be : (

g =

acceleration due to gravity on the surface of earth)

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Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A rocket fired vertically with a speed of

4 km s^{- 1}

from the earth's surface. How far from the earth does the rocket go before returning to the earth?
(Take radius of earth

= 6.4 \times 10^{6} m

and

g = 10 m s^{- 2}

)

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

An object is propelled vertically to a maximum height of,

4 R

from the surface of a planet of radius,

R

and mass

M

. The speed of object when it returns to the surface of the planet is

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A body of mass

m

is moving in a circular orbit of radius

R

about a planet of mass

M

. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius

\frac{R}{2}

. And the other mass, in a circular orbit of radius

\frac{3 R}{2} .

The difference between the final and the initial total energies is

Important Questions on Gravitation

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