Gravitation practice · Medium

Assertion: The work done to project a body of mass $m$ from the earth's surface (radius $R$ ) to infinity is $m g R$.

Reason: The required work done is equal to change in potential energy of the mass, which is equal to $G M m / R$.

Two satellites of mass $m\,and\,9m$ are orbiting a planet in orbit of radius R. Their periods of revolution will be in the ratio of

If the earth rotates faster than its present speed, the weight of an object will

If $R$ is the radius of the orbit of a geosynchronous satellite and another satellite is orbiting around the earth in a circular orbit of radius $\frac{R}{2}$, then its time period would be

Assertion: An astronaut experience weightlessness in a space satellite.

Reason: When a body falls freely it does not experience gravity.

Assertion: If Earth were a hollow sphere, gravitational field intensity at any point inside the Earth would be zero.
Reason: Net force on a body inside the sphere is zero.

In reference to geostationary satellite, which
among the following is correct?

At a height of $10 \mathrm{~km}$ above the surface of earth, the value of acceleration due to gravity is the same as that of a particular depth below the surface of earth. Assuming uniform mass density of the earth, the depth is

If a planet of given density were made larger its force of attraction for an object on its surface would increase because of planet’s greater mass but would decrease because of the greater distance from the object to the centre of the planet. Which effect predominate?

Determine the energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 3R.

A satellite is moved from one circular orbit around the earth to another of lesser radius. Which of the following statement is true?

The mass of a planet is twice the mass of earth and diameter of the planet is thrice the diameter of the earth, then the acceleration due to gravity on the planet's surface is

The escape velocity from the Earth’s surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is

The moon’s radius is $\frac{1}{4}$ that of the earth and its mass is $\frac{1}{{80}}$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Earth has atmosphere whereas moon doesn't have any atmosphere.

Reason R: The escape velocity on moon is very small as compared to that on earth.

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

A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

A planet revolves round the Sun in an elliptical orbit with the Sun at one of the foci. Regarding the speed and velocity of the planet which of the following is correct?

(A): The angular velocity of a planets orbiting around the sun increases when they are nearest to the sun.
(R): The angular momentum of body is proportional to angular velocity.

To remove an object from earth's gravitational field the speed that is to be given to it on the surface of the earth is nearly equal to $11.25 \mathrm{~km} / \mathrm{s}$. However, when an object on the earth is to be removed from the solar system, gravitational influence of the sun is taken in account. To remove an object from the solar system, the speed that is given to it on earth's surface is nearly equal to $45 \mathrm{~km} / \mathrm{s}$. The mass of the sun is $\mathrm{k}_1$ times the mass of the earth and the orbital radius of the earth is $\mathrm{k}_2$ times its radius. Find the value of $\mathrm{k}_1 / \mathrm{k}_2$.

Assertion: On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not feel weightlessness on moon.

Reason: Mass of moon is considerable.

Acceleration due to gravity at earth's surface is $10 \mathrm{~ms}^{-2}$. The value of acceleration due to gravity at the surface of a planet of mass $\frac{1}{5}$ th and radius $\frac{1}{2}$ of the earth is -

Earth binds the atmosphere because of

The Earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the Earth. The escape velocity of a body from this platform is $fv$, where $v$ is its escape velocity from the surface of the Earth. The value of f is

A man weighs $\mathrm{W}$ on the surface of the earth. What is his weight at a height equal to $\mathrm{R}$ ? $\mathrm{R} \rightarrow$ Radius of earth)

Which of the following statement is always correct about a planet revolving around sun?

If the force inside the earth surface varies as ${x^n}$, where $r$ is the distance of body from the centre of earth, then the value of $n$ will be

Assertion: A person feels weightlessness in an artificial satellite of the earth. However a person on the moon (natural satellite) feels his weight.
Reason: Artificial satellite is a freely falling body and on the moon surface, the weight is mainly due to moon's gravitational attraction.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.
Reason R : The product of their mass and radius must be same, ${M_1}{R_1} = \mathrm{ }{M_2}{R_2}$
In the light of the above statements, choose the most appropriate answer from the options given below.

Which of the following statements is true:

Assertion: When distance between two bodies is doubled and mass of each body is also doubled, gravitational force between them remains the same.
Reason: According to Newton’s law of gravitation, force is directly proportional to mass of bodies and inversely proportional to square of distance between them.