EASY

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A uniform solid sphere of radius $R$ produces a gravitational acceleration of $a_{o}$ on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes $\frac{a_{o}}{4}$ is,

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Important Questions on Gravitation

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Which of the following most closely depicts the correct variation of the gravitation potential,

V (r)

with distance

r

due to a large planet of radius

R

and uniform mass density? (figures are not drawn to scale)

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

V

is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

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:

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

A solid sphere of radius $R$ gravitationally attracts a particle placed at $3 R$ from its centre with a force $F_{1} .$ Now a spherical cavity of radius $(\frac{R}{2})$ is made in the sphere (as shown in figure) and the force becomes $F_{2}$ . The value of $F_{1} : F_{2}$ is:

Question Image

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

A rocket is fired from the earth to the moon. The distance between the earth and the moon is

r

and the mass of the earth is

81

times the mass of the moon. The gravitational force on the rocket will be zero when its distance from the moon is,

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

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8} R$ is the distance between the centres of a ring (of mass $m$ ) and a sphere (mass $M$ ) where both have equal radius $R$

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MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Inside a uniform spherical shell :

(a) The gravitational field is zero.

(b) The gravitational potential is zero.

(d) The gravitation potential is the same everywhere.

(e) All the above.

Choose the most appropriate answer from the options given below:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Two particles of identical mass are moving in circular orbits under a potential given by

V (r) = K r^{- n}

, where

K

is a constant. If the radii of their orbits are

r_{1}, r_{2}

and their speeds are

v_{1}, v_{2}

respectively, then

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Consider a spherical gaseous cloud of mass density

ρ (r)

in free space where

r

is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy

K

. The force acting on the particles is their mutual gravitational force. If

ρ (r)

is constant in time, the particle number density

n (r) = ρ (r) / m

is: [

G

is universal gravitational constant]

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 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 gravitational field in a region is given by

\vec{g} = (5 \hat{i} + 12 \hat{j}) N {kg}^{- 1}

. The change in the gravitational potential energy of a particle of mass

2 kg

when it is taken from the origin to a point

(7 m, - 3 m)

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

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 mass of

50 kg

is placed at the center of a uniform spherical shell of mass

100 kg

and radius

50 m

. If the gravitational potential at a point,

25 m

from the center is

V kg m^{- 1}

. The value of

V

is:

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

The mass density of a planet of radius

R

varies with the distance

r

from its centre as

ρ (r) = ρ_{0} (1 - \frac{r^{2}}{R^{2}})

, then the gravitational field is maximum at:

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

Consider two solid spheres of radii $R_{1} = 1 m$ , $R_{2} = 2 m$ and masses $M_{1}$ and $M_{2},$ respectively. The gravitational field due to sphere $(1)$ and $(2)$ are shown. The value of $\frac{M_{1}}{M_{2}}$ is:

Question Image

A uniform solid sphere of radius R produces a gravitational acceleration of ao on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes ao4 is,

Important Questions on Gravitation

Learn and Prepare for any exam you want !

A uniform solid sphere of radius $R$ produces a gravitational acceleration of $a_{o}$ on its surface. The distance of the point from the centre of the sphere where the gravitational acceleration becomes $\frac{a_{o}}{4}$ is,