Gravitation practice · Medium

Which of the following is/are correct.

I. An object moving the earth under the influence of Earth's gravitational force is in a state of "free-fall".

II. The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

III. Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very large height.

IV. The path of a projectile is independent of the gravitational force of earth.

The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity

If the radius of the earth decreases by 10%, the mass remaining unchanged, then the acceleration due to gravity.

The ratio of the radii of the planets ${P_1}\,and\,{P_2}$ is a. The ratio of their acceleration due to gravity is b. The ratio of the escape velocities from them will be

Observers on the 10th, 5th and ground floor of a tall building measure the velocity of a certain raindrop by some accurate method. Surprisingly the velocity of the raindrop measured by the three observers was found to be the same. This is because

The orbital velocity of a body close to the earth's surface is

Assertion: Gravitational force between two particles is negligibly small compared to the electrical force.
Reason: The electrical force is experienced by charged particles only.

When earth moves around the sun, the quantity which remains constant is

Abody weighed $250 \mathrm{~N}$ on the surface assuming the earth to be a sphere of uniform mass density, how much would it weigh half way down to the centre of the earth?

The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as

Statement I: At height $h$ from ground and at depth $h$ below ground, where $h$ is approximately equal to $0.62 \mathrm{R}$, the value of $\mathrm{g}$ acceleration due to gravity is same.

Statement II: Value of $\mathrm{g}$ decreases both sides, in going up and down.

A point $P\left( {R\sqrt 3 ,0,0} \right)$ lies on the axis of a ring of mass $M$ and radius $R$. The ring is located in $y - z$ plane with its centre at origin $O$. A small particle of mass m starts from P and reaches $O$ under gravitational attraction only. Its speed at $O$ will be

The radius of the earth is $6.37 \times 10^6 \mathrm{~m}$, its mean density is $5.5 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and $G=6.66 \times 10^{-11}\mathrm{~Nm}^2 \mathrm{~kg}^{-2}$. Determine the gravitational potential on the surface of the earth.

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is

Consider the following statements and select the correct statement(s).
(i) Gravitational force may be attractive or repulsive.
(ii) Gravitational force between two particles is independent of presence of other particles.
(iii) Gravitational force is a short-range force.

At a point above the surface of the earth, the gravitational potential is $-5.12 \times 10^7 \mathrm{~J} \mathrm{~kg}^{-1}$ and the acceleration due to gravity is $6.4 \mathrm{~ms}^{-2}$. Assuming the mean radius of the earth to be $6400 \mathrm{~km}$, calculate the height of this point above the earth's surface.

In a satellite orbiting the earth, a coin is immersed in a jar of
water and released. It will:

Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

A satellite is in an orbit around the Earth; if its kinetic energy is doubled, then

An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre of the earth. Where radius of earth, $R=6400 \mathrm{~km}$. The percentage decrease in the weight of the object will be

Statement I: Escape velocity of a tennis ball from the surface of earth is the same as the escape velocity of a cricket ball from the surface of earth.

Statement II: Escape velocity of a body is independent of the mass of the body

Two masses 2 kg and 4 kg are separated in air by 10 cm. Now air is replaced by water of density $1000\,kg/{m^3}$, then the percentage change in force is

A man is standing on an international space station, which is orbiting earth at an altitude 520 Km with a constant speed 7.6 km/s. If the man’s weight is 50 kg, his acceleration is [in $m/{s^2}$]

To what height the body is to be raised so that acceleration due to gravity on it is 1% of the value on the surface of earth? (Radius of earth is 6400km)

At what depth below the surface of the earth, the value of $g$ is the same as that at a height of 5 km?

Orbital velocity of an artificial does not depend upon

Given below are two statements:
Statement I: Acceleration due to gravity is different
at different places on the surface of earth.
Statement II: Acceleration due to gravity increases
as we go down below the earth’s surface.
In the light of the above statements, choose the correct answer from the options given below

The international space station is maintained in a nearly circular orbit with a mean altitude of $330 \mathrm{~km}$ and a maximum of $410 \mathrm{~km}$. An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is

If the radius of earth reduces by $4 \%$ and density remains same then escape velocity will