Gravitation practice · Mixed difficulty

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to

The height above surface of earth where the value of gravitational acceleration is the value of
gravitational acceleration is one fourth of that at surface, will be

If the mass of a body on the earth surface is $M$, then its mass on the moon surface, is

The acceleration of a train travelling with speed of 400 m/s as it goes round a curve of radius 160 m, is

What does not change in the field of central force

Pertaining to two planets, the ratio of escape velocities from respective surfaces is $1: 2$, the ratio of the time period of the same simple pendulum at their respective surfaces is $2: 1$ (in same order). Then the ratio of their average densities is

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is

Given below are two statements:

Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity $(\mathrm{g})$.

Statement II : The effect of rotation of the earth on the value of ' $g$ ' at the equator is minimum and that at the pole is maximum.

In the light of the above statements, choose the correct answer from the options given below

Two spherical balls of mass 1 kg and 4 kg are separated by a distance of 12 cm. The distance from 1 kg at which the gravitational force on any mass becomes zero.

The escape velocity from the earth is $11.2\;\mathrm{kms}{\;^{ - 1}}$. The escape velocity from a planet having twice the radius and the same mean density is $(\mathrm{in\;km}{\mathrm{s}^{ - 1}})$

According to Newton's law of gravitation, the magnitude of the force $F$ on point masses $m_1$ and $m_2$ (say) is given by $|F|=\frac{G m_1 m_2}{r^2}$.
I. This equation is not directly applicable for the gravitational force between extended object (like the earth) and a point mass.
II. This equation can be applied to find the gravitational force between an extended object and a point mass provided $r$ is the distance of the point mass from the geometric centre of the extended objects.
Which of the following statement(s) about this equation is/are correct?

If ${W_1},{W_2}\,\,\mathrm{and}\,\,{W_3}$ represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively, (as shown in the figure) in the gravitational field of a point mass $m$, find the correct relation between ${W_1},{W_2}\,\,\mathrm{and}\,\,{W_3}$ .

Time period of a simple pendulum inside a satellite orbiting Earth is:

Period of revolution of a geostationary satellite around the earth is

Where will it be profitable to purchase 1 kilogram sugar

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

Select the incorrect statements from the following.
(i) The orbital velocity of a satellite increases with the radius of the orbit.
(ii) Escape velocity of a particle from the surface of the Earth depends on the speed with which it is fired.
(iii) The time period of a satellite does not depend on the radius of the orbit.
(iv) The orbital velocity is inversely proportional to the square root of the radius of the orbit.

When does the object in a satellite escapes to infinity?

A rocket is launched vertical from the surface of the earth of radius $R$ with an initial speed $v$. If atmospheric resistance is neglected, then maximum height attained by the rocket is

If the escape velocity on the earth is 11.2 Km/s, its value for a planet having double the radius and 8 times the mass of the earth is …… (in km/s)

Assertion: Gravitational forces do not depend on the medium between the masses.
Reason: Mediating particle responsible for gravitational force is graviton.

Two spheres of mass $m$ and M are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

Assertion: The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth.
Reason: The value of acceleration due to gravity is minimum at the equator and maximum at the pole.

A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2 $\mathrm{rad\;}{\mathrm{s}^{ - 1}}$. The centripetal force, is

The maximum and minimum distances of a comet from the sun are $8 \times {10^{12}}m$ and $1.6 \times {10^{12}}m$ . If its velocity when nearest to the sun is $60\,\,m/s$ . What will be its velocity in $m/s$ , when it is farthest?

Assertion: Smaller the orbit of a planet around the sun, shorter is the time it takes to complete.
Reason: According to Kepler's third law of planetary motion, square of time period is proportional to cube of mean distance from the sun.

The value of $g$ on the surface of earth is smallest at the equator because

Assertion: Earth does not retain hydrogen molecules and helium atoms in its atmosphere, but does retain much heavier molecules, such as oxygen and nitrogen.
Reason: Lighter molecules in the atmosphere have translational speed that is greater or closer to escape speed of earth.

The escape velocity from the earth is $11\,\,km/s$ . The escape velocity from a planet having twice the radius and same density as that of the earth is (in $km/s$ )

Kepler's law states that, square of the time period of any planet moving around the sun in an elliptical orbit of semi-major axis $(R)$ is directly proportional to