Gravitation practice · Mixed difficulty

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".

If $\rho$ is the density of the planet, the time period of nearby satellite is given by

Newton’s universal law of gravitation applies to

The height above the earth’s surface at which the acceleration due to gravity becomes 9% of its value at the surface is ($R$ is radius of earth)

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}\,and\,{W_3}$ respectively, then

For a satellite orbiting in an orbit, close to the surface of Earth, to escape, what is the percentage increase in the kinetic energy required?

Two small bodies of masses $10 \mathrm{~kg}$ and $20 \mathrm{~kg}$ are kept a distance $1.0 \mathrm{~m}$ apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to $0.5 \mathrm{~m}$.

If $v_o$ be the orbital velocity of a satellite in a circular orbit close to the earth's surface and $v_e$ is the escape velocity from the earth, then relation between the two is

Orbital velocity of earth satellite does not depend on

Assertion: The acceleration of a particle near the earth surface differs slightly from the gravitational acceleration $a_g = GM/R^2.$
Reason: The earth is not a uniform sphere and because the earth rotates.

Two satellites of same mass are launched in the same orbit of radius $r$ around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is

Gravitational acceleration on the surface of a planet is $\frac{{\sqrt 6 }}{{11}}\mathrm{\;}g,\;$, where $g$ is the gravitational acceleration on the surface of earth. The average mass density of the planet is $\frac{2}{3}$ times
that of the earth. If the escape speed on the surface of the earth is taken on be $11\mathrm{\;km}{\mathrm{s}^{ - 1}},$
the escape speed on the surface of the planet in $\mathrm{km}{\mathrm{s}^{ - 1}}\mathrm{\;}$ will be

A body of mass $m$ is projected from earth surface with speed ${v = \,2\sqrt {gR} }$ (where $R$ is the radius of earth). Find its speed at very far (infinite) from earth’s surface:-

The gravitational force between two point masses ${m_1}\,and\,{m_2}$ at separation $r$ is given by $F = k\frac{{{m_1}{m_2}}}{{{r^2}}}$. The constant $k$

For a uniform ring of mass $M$ and radius $R$ at its centre,

Assertion: Plane of space satellite is always equatorial plane.

Reason: On the equator value of $g$ is minimum.

Assertion: Plane of geostationary satellites always passes through equator.

Reason: Geostationary satellites always lies above Moscow.

If the earth stops rotating about its own aixs, $g$ remains unchanged at

The gravitation field in a region is given by $\overrightarrow g = 5N/kg\hat i\, + \,12N/kg\hat j.$ The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point (7 m, -3 m) is:

Gravitational potential is expressed as $V = m{x^2}$ field at $x = 1m$ is (in S.I)