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If the kinetic energy of a satellite orbiting around the earth is doubled then

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Important Questions on Gravitation

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A body is projected upwards with a velocity of

4 \times 11.2 km s^{- 1}

from the surface of earth. The velocity of the body when it escapes the gravitational pull of earth is

MEDIUM

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

Two satellites,

A

and

B

, have masses

m

and

2 m

respectively.

A

is in a circular orbit of radius

R

and

B

is in a circular orbit of radius

2 R

around the earth. The ratio of their kinetic energies,

\frac{K_{A}}{K_{B}}

is:

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

MEDIUM

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions,

A, B

and

C

are

K_{A}, K_{B} a n d K_{C}

, respectively.

A C

is the major axis and

S B

is perpendicular to

A C

at the position of the Sun

S

as shows in the figure. Then

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EASY

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A satellite is orbiting the Earth in a circular orbit of radius

R

. Which one of the following statements is true?

HARD

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is $S .$

EASY

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

Binding energy of a revolving satellite at height

h

3.5 \times 10^{8} J

. Its potential energy is

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

The energy required to take a satellite to a height

h

above the Earth surface (radius of Earth

= 6.4 \times 10^{3} km

) is

E_{1}

, and the kinetic energy required for the satellite to be in a circular orbit at this height is

E_{2} .

The value of

h

for which

E_{1}

and

E_{2}

are equal, is

HARD

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

An asteroid is moving directly towards the centre of the earth. When at a distance of

10 R

(

R

is the radius of the earth) from the centre of the earth, it has a speed of

12 km s^{- 1} .

Neglecting the effect of earth's atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is

11.2 k m s^{- 1})

? Give your answer to the nearest integer in

km s^{- 1}

__________.

HARD

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A body is thrown from the surface of the earth with velocity

u m s^{- 1}

. The maximum height in meter above the surface of the earth up to which it will reach is (

R =

radius of the earth,

g =

acceleration due to gravity)

MEDIUM

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A stationary object is released from a point

P

a distance

3 R

from the centre of the moon which has radius

R

and mass

M

. Which one of the following expressions gives the speed of the object on hitting the moon?

HARD

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

Two stars of masses

3 \times 10^{31} kg

each, and at distance

2 \times 10^{11} m

rotate in a plane about their common centre of mass

O .

A meteorite passes through

O

moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at

O

is ( Take Gravitational constant

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

)

HARD

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

Suppose two planets (spherical in shape) of radii $R$ and $2 R,$ but mass $M$ and $9 M$ respectively have a centre to centre separation $8 R$ as shown in the figure. A satellite of mass $m$ is projected from the surface of the planet of mass $M$ directly towards the centre of the second planet. The minimum speed $v$ required for the satellite to reach the surface of the second planet is $\sqrt{\frac{a}{7} \frac{G M}{R}}$ , then the value of $a$ is
[Given : The two planets are fixed in their position]

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A remote-sensing satellite of earth revolves in a circular orbit at a height of

0.25 \times 10^{6}

m above the surface of earth. If earth's radius is

6.38 \times 10^{6} m

and

g = 9.8 m s^{- 2}

, then the orbital speed of the satellite is:

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

If the axis of rotation of the earth were extended into space then it would pass close to -

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

The relative uncertainty in the period of a satellite orbiting around the earth is

10^{- 2}

. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is:

EASY

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

A satellite is orbiting close to the earth and has a kinetic energy

K

. The minimum extra kinetic energy required by it to just overcome the gravitation pull of the earth is

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Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

The ratio of the binding energy of a satellite at rest on earth's surface to the binding energy of a satellite of same mass revolving around the earth at a height

h

above the earth's surface is

(R

= radius of the earth

)

MEDIUM

Physics>Mechanics>Gravitation>Energy of an Orbiting Satellite

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

m

from the surface of a planet of mass

M

and radius

R

in a circular orbit at an altitude of

2R

If the kinetic energy of a satellite orbiting around the earth is doubled then

Important Questions on Gravitation

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