HARD

Earn 100

From a solid sphere of mass M and radius R, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in diagram. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the centre of the cavity thus formed is: (G = Gravitational constant)

45.16% studentsanswered this correctly

Important Questions on Gravitation

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

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

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

MEDIUM

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

On the

x

-axis and at a distance

x

from the origin, the gravitational field due to a mass distribution is given by

\frac{a x}{{(x^{2} + a^{2})}^{3 / 2}}

in the

x

-direction. The magnitude of the gravitational potential on the

x

-axis at a distance

x

, taking its value to be zero at infinity is:

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

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),

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

Two bodies of masses

m

and

4 m

are placed at a distance

r

. The gravitational potential at a point on the line joining them where the gravitational field is zero is

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

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)

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:

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

A particle of mass

M

is situated at the centre of a spherical shell of same mass and radius

a

. The magnitude of the gravitational potential at a point situated at

\frac{a}{2}

distance from the centre, will be

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]

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

A spherically symmetric gravitational system of particles has mass density $ρ = \{\begin{cases} ρ_{0} for r \leq R \\ 0 for r > R \end{cases}$ where, $ρ_{0}$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $v$ as a function of distance $r (0 < r < \infty)$ from the centre of the system is represented by

HARD

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:

EASY

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

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

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 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-

HARD

Physics>Mechanics>Gravitation>Gravitational Potential and Potential Energy

From a solid sphere of mass $M$ and radius $R,$ a spherical portion of radius $(\frac{R}{2})$ is removed as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the centre of the cavity thus formed is ( $G =$ gravitational constant)

Question Image

From a solid sphere of mass M and radius R, a spherical portion of radius R2 is removed, as shown in diagram. Taking gravitational potential V=0 at r=∞, the potential at the centre of the cavity thus formed is: (G = Gravitational constant)

Important Questions on Gravitation

Learn and Prepare for any exam you want !

From a solid sphere of mass M and radius R, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in diagram. Taking gravitational potential $V = 0$ at $r = \infty,$ the potential at the centre of the cavity thus formed is: (G = Gravitational constant)