Gravitation practice · Medium

Halley’s comet has a period of 76, had distance of closest approach to the sun equal to $8.9 \times {10^{10}}\mathrm{m}$. the comet’s farthest distance from the sun if the mass of sun is $2 \times {10^{30}}kg\,and\,G = 6.67 \times {10^{11}}$ in MKS units is

Find the sum of given series

$F=\frac{G M m}{r^2}\left[\left.1+\frac{1}{2}+\frac{1}{4}+\ldots \infty \right\rvert\,\right]$

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole

The value of ${G}$ varies with

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth $=R$ )

Assertion: Gravitational potential is maximum at infinite.
Reason: Gravitational potential is the amount of work done to shifting a unit mass from infinity to a given point in gravitational attraction force field.

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

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 $(\mathrm{in\;km}{\mathrm{s}^{ - 1}})$

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:

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?

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

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 $km/s$ )