Gravitation practice · Mixed difficulty

A chain of 125 links is 1.25 m long and has mass of 2 kg with the ends fastened together. It is set for rotating at 50 $\mathrm{rev}{\mathrm{s}^{ - 1}}$, centripetal force on each links is

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

Statement-1: The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero.
Statement-2: The gravitation field due to the shell inside the shell will be zero.

If the earth stops rotating, the value of $g$ at the equator

According to Kepler's law of planetary motion, if $T$ represents time period and $r$ is orbital radius, then for two planets these are related as

An iron ball and a wooden ball of the same radius are released from a beight $h$ in vacuum. The time taken by both to reach the ground is. The correct option is:

A mass ' $\mathrm{m}$ ' suspended from a spring stretches it by $5 \mathrm{~cm}$ when on the surface of the earth. The mass is then taken on to a height of $1600 \mathrm{~km}$ above earth's surface and again suspended from the same spring. At this altitude the extension of the spring is (Radius of earth = $6400 \mathrm{~km}$)

Astronaut is in a stable orbit around the earth when he weighs a body of mass 5 kg. What is reading of spring balance?

Gravitational potential of the body of mass $m$ at a height $h$ from surface of earth of radius $R$ is (Take $g=$ acceleration due to gravity at earth's surface).

If the rotational motion of earth about its axis
increases, then the weight of a body on equator
would

A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy

A satellite of mass m is circulation around the earth with constant angular velocity. If radius of the orbit is ${R_0}$ and mass of the earth M, the angular momentum about the centre of the earth is

Satellite A and B are revolving around the orbit of earth. The mass of A is 10 times of mass of B.The ratio of time period $\left( {\frac{{{T_A}}}{{{T_B}}}} \right)$ is

Assertion(A): Areal velocity of a planet around sun will become two times, if mass of planet is halved.
Reason(R): Areal velocity $=\frac{L}{2 m}$, where $L$ is angular momentum of planet about centre of sun.

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.

If the speed of rotation of earth about its axis increases, then the weight of the body at the equator will

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