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The minimum speed at which an object of $1 kg$ mass is thrown from the surface of the moon so that it does not fall back to the moon is

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Important Questions on Gravitation

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Given below are two statements : one is labelled as Assertion $A$ and the other is labelled as Reason $R$ .

Assertion $A$ : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.

Reason $R$ : The product of their mass and radius must be same. $M_{1} R_{1} = M_{2} R_{2}$ In the light of the above statements, choose the most appropriate answer from the options given below :

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

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

Consider a star of one solar mass. If only light can escape from the surface of the star, then the ratio of the radius of the star to that of the sun is(consider the star to be spherical and uniformly dense. Escape velocity on the surface of the sun is approximately

600 km s^{- 1}

, speed of light

= 3 \times 10^{8} m s^{- 1}

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?

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Consider two spherical planets $A$ and $B$ with radii

R_{A}

and

R_{B}

respectively. If

R_{A} = 2 R_{B}

and the escape velocities at the two planets

V_{escape}^{A}

and

V_{escape}^{B}

are equal, then the ratio of densities of $A$ and $B$,

ρ_{A} : ρ_{B}

is (consider $A$ and $B$ to be uniformly dense)

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

The escape velocity from the Earth's surface is

v

. The escape velocity from the surface of another planet having a radius four times that of Earth and the same mass density is:

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

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 :

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A spherically uniform planet of $mass 8 \times 10^{24} kg$ and or radius $6 \times 10^{6} m$ is orbiting around the Sun. The escape velocity for the planet is close to (Take, $G = 6 \times 10^{- 11} N - m^{2} / {kg}^{2})$

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

The velocity of escape on a planet whose radius is

1.7 \times 10^{6} m

and acceleration due to gravity is

1.7 m / s^{2}

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The radius in kilometer to which the present radius of earth

(R = 6400 km)

to be compressed so that the escape velocity is increased

10

time is _______.

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

What should be the closest approximate radius of a celestial body twice as massive as the sun so that escape speed from the celestial body is equal to the speed of light? (The mass of sun is

2 \times 10^{30} kg

, speed of light

3 \times 10^{8} m s^{- 1}

, and universal gravitational constant

G = 7 \times 10^{- 11} N m^{2} {Kg}^{- 2}

)

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Identify the correct expression between radius

(R),

density

(ρ)

and the escape velocity from the surface

(v_{e})

of a planet.

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The masses and radii of the earth and moon are

(M_{1}, R_{1})

and

(M_{2}, R_{2})

respectively. Their centres are at a distance

r

apart. Find the minimum escape velocity for a particle of mass

m

to be projected from the middle of these two masses :

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)

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:

The minimum speed at which an object of 1 kg mass is thrown from the surface of the moon so that it does not fall back to the moon is

Important Questions on Gravitation

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The minimum speed at which an object of $1 kg$ mass is thrown from the surface of the moon so that it does not fall back to the moon is