Gravitation practice · Mixed difficulty

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.

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on

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 $m/{s^2}$]

Assertion: If a particle projected horizontally just above the surface of earth with a speed greater than escape speed, then it will escape from gravitational influence of earth.
Reason: Escape velocity is independent of its direction.

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?

The imaginary angular velocity of the earth for which the effective acceleration due to gravity at the equator shall be zero is equal to
(Take, $g=10 \mathrm{~ms}^{-2}$ for the acceleration due to gravity, if the earth were at rest, radius of earth equal to $6400 \mathrm{~km}$ and $\lambda=60$ )

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

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

Statement-1: A planet is moving around the sun in an elliptical orbit. Then from aphelion point to perihelion point the speed of the planet continuously increases.
Statement-2: According to Kepler's second law, the areal velocity of the line joining planet to the sun is constant.

Statement-1: Orbiting satellite or body has K.E. of always less than that of Potential energy.
Statement-2: For any bound state, the magnitude of potential energy is always twice that of kinetic energy (K.E.)

Earth orbiting satellite will escape, if

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{G M_e m}{21 R_e}$. The value of $x$ is (take $\left.{R}_{{e}}=6370 \mathrm{~km}\right)$:

A body is projected from earth's surface to become its satellite, its time period of revolution will not depend upon

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.

The weight of the body at the centre of the earth is