Gravitation practice · Medium

Two isolated point masses ${m}$ and ${M}$ are separated by a distance $\ell$. The moment of inertia of the system about an axis passing through a point where gravitational field is zero and perpendicular to the line joining the two masses, is

Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is $2 F.$ The space around the masses is now filled with a liquid of specific gravity 4. The gravitational force will now be

A satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears, the satellite will

The gravitational attraction between the two bodies increases when their masses are

An artificial satellite of mass ‘m’ is revolving round the earth in a circle of radius $R$. Then work done in one revolution is

Six stars of equal mass $m$ are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length a. Their common time period of revolution around center will be

Assertion: If the earth stops rotating about its axis, the value of the weight of the body at equator will decrease.
Reason: The centripetal force does not act on the body at the equator.

What is the energy required to launch a $m \mathrm{~kg}$ satellite from earth's surface to a circular orbit at an altitude of $7 R$? ($R=$ radius of the earth)

Satellite A and B are revolving around the orbit of earth. The mass of A is 10 times of mass of B.The ratio of time period $\left( {\frac{{{T_A}}}{{{T_B}}}} \right)$ is

The Earth's gravity provides the centripetal force on a orbiting satellite to keep it moving in circle at constant speed. Which statements best explains why the speed of the satellite does not change even through there is a net force exerted on it?

If the angular speed of earth is increased so much that the objects start flying from the equator, then the length of the day will be nearly

A mass $M$ is broken into two parts of masses $m_1$ and $m_2$. How are $m_1$ and $m_2$ related so that force of gravitational attraction between the two parts is maximum?

Satellite A and B are revolving around the orbit of earth. The mass of A is 10 times of mass of B.The ratio of time period $\left( {\frac{{{T_A}}}{{{T_B}}}} \right)$ is

Two identical trains $P$ and $Q$ move with equal speeds on parallel tracks along the equator. $P$ moves from east to west and $Q$ from west to east

A planet revolving in elliptical orbit has
I. a constant velocity of revolution
II. has the least velocity when it is nearest to the sun
III. its areal velocity is directly proportional to its velocity.
IV. areal velocity is inversely proportional to its velocity.
V. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below.

A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

The length of a seconds pendulum if it is placed at height $2 R$ ($R$ : radius of earth) is $\frac{10}{x \pi^2}$ metres. Find $x$.

Three particles each of mass $m$ are kept at the vertices of an equilateral triangle of side $L$. The gravitational field at, centre due to these particles is

Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors :
I. Mass of the planet
II. Mass of the particle escaping
III. Temperature of the planet
IV. Radius of the planet
Select the correct answer from the codes given below :

If suppose moon is suddenly stopped and then released (given radius of moon is one-fourth the radius of earth)and the acceleration of moon with respect to earth is $0.0027\,\mathrm{m}{\mathrm{s}^{ - 2}}$), then the acceleration of the moon just before striking the earth’s surface is (Take $g = 10m{s^{ - 2}})$

Two particles of masses $m$ and $M$ are initially at rest at infinite distance. Find their relative velocity of approach due to gravitational attraction when $d$ is their separation at any instant.

Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be

Masses 1 kg and 4 kg are 6 cm apart. The point along the line joining the masses where the gravitational field due to them is zero is

A satellite is orbiting very close to surface of the earth. Its time period is approximately

If $M$ is the mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is

Spot the wrong statement:
The acceleration due to gravity 'g' decreases if

What is the distance of a geostationary satellite from the Earth's centre?

The escape velocity of an object on a planet whose radius is 4times that of the earth and '$g$' value 9 times that on the earth, in $km{s^{ - 1}}$ is

The escape velocity of a body depends upon mass as

STATEMENT-1: An astronaut in an orbiting space station above the earth experiences weightlessness. because

STATEMENT - 2 : An object moving the earth under the influence of Earth's gravitational force is in a state of "freefall".