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A binary star is a system of two stars moving around the centre of mass of the system due to mutual gravitational force. The total mass of two stars $= M_{0}$ and the period of revolution is $T$ . Find the distance in $km$ between stars? (Take $G M_{0} = 8 \times 10^{6} SI unit$ and $T = 2 π \times 10^{3}$ seconds).

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Important Questions on Gravitation

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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

R

. Which one of the following statements is true?

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A satellite of mass

m

is orbiting the earth (of radius

R

) at a height

h

from its surface. The total energy of the satellite in terms of

g_{o}

, the value of acceleration due to gravity at the earth's surface, is

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A test particle is moving in a circular orbit in the gravitational field produced by a mass density

ρ (r) = \frac{K}{r^{2}} .

Identify the current relation between the radius

R

of the particle’s orbit and its period

T :

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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:

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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}

__________.

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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

)

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A body is moving in a low circular orbit about a planet of mass

M

and radius

R

. The radius of the orbit can be taken to be

R

itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

The minimum number of geostationary satellites required for uninterrupted global coverage is

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A spaceship orbits around a planet at a height of

20 k m

from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in

24

hours around the planet?
[Given: Mass of planet

= 8 \times 10^{22} k g

,
Radius of planet

= 2 \times 10^{6} m,

Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} / k g^{2}

]

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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:

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A satellite is revolving in a circular orbit at a height

h

from the earth's surface (radius of earth

R

;

h << R

). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to (Neglect the effect of atmosphere.)

HARD

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

The mass density of a spherical galaxy varies as

\frac{K}{r}

over a large distance

r

from its center. In that region, a small star is in a circular orbit of radius

R

. Then the period of revolution,

T

depends on

R

as:

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

In an earth satellite moving in a circular orbit, a piece of metal (weighing

0.016 kg

on the earth) is weighed by a spring balance while the metal is suspended in water. If the density of metal is

8

times of water density, then the recorded weight will be (g is acceleration due to gravity)

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

A planet is moving in a circular orbit. It completes

2

revolutions in

360 days

. What is its angular frequency?

EASY

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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:

MEDIUM

Physics>Mechanics>Gravitation>Motion of Planets and Satellites

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>Motion of Planets and Satellites

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}

)

A binary star is a system of two stars moving around the centre of mass of the system due to mutual gravitational force. The total mass of two stars =M0 and the period of revolution is T. Find the distance in km between stars? (Take GM0=8×106 SI unit and T=2π×103seconds).

Important Questions on Gravitation

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