Gravitation practice · Mixed difficulty

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

Assertion (A): Angular momentum conservation can be used to explain Kepler's second law of planetary motion.

Reason (R): Areal velocity of a planet revolving around the sun is equal to its angular momentum.

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

A particle would take a time $t$ to move down a straight tube from the surface of earth (supposed to be a homogeneous sphere) to its centre. If gravity were to remain constant, then the time would be $t$. The ratio of $t / t^{\prime}$ will be

The distance of a geo-stationary satellite from the centre of the earth (Radius R=6400 km) is nearest to

Orbital velocity of earth satellite does not depend on

The earth revolves around the sun in one year. If the distance between them becomes double, the new period of revolution will be

Two planets have same radii and different uniform densities. The acceleration due to gravity on surface would be

Two planets, A and B are orbiting a common star in circular orbits of radii $\mathrm{R_A}$ and $\mathrm{R_B},$ respectively, with $\mathrm{R_B=2 R_A}.$ The planet B is $4 \sqrt{2}$ times more massive than planet A. The ratio $\mathrm{\left(\frac{L_B}{L_A}\right)}$ of angular momentum $\left(\mathrm{L_B}\right)$ of planet B to that of planet $\mathrm{A\left(L_A\right)}$ is closest to integer ______

$2 \mathrm{~kg}$ body falls from infinity to the surface of earth what will be the kinetic energy of the body on reaching the surface of Earth? (Assume escape velocity to be $10^{24} \mathrm{~J}$

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.

If mass of a body is M on the earth surface, then the mass of the same body on the moon surface 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?

A body is released from height equal to radius R of the earth. The velocity of body with which it will strike the earth surface is

If a planet of given density were made larger (keeping its density unchanged) its force of attraction for an object on its surface would increase because of increased mass of the planet but would decrease because of larger separation between the centre of the planet and its surface. Which effect would dominate?

The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. If $V_P$ and $V_E$ are escape velocities of the planet and the earth, respectively, then

S-I: The moon moves around the earth in a circular orbit and the earth moves around the sun in elliptical orbit then.
S-II: The sun's attraction on the earth and moon are external force acting on the centre of mass of the system

The time period of revolution of a planet ‘A’ around the sun is 27 times that of another planet ‘B’. The ratio of distance of planet ‘B’ to the planet ‘A’ from sun

The value of ' $\mathrm{g}$ ' on poles is

An astronaut of mass m is working in a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull ${F_G}$ on the astronaut is

Consider a binary star system of star $A$ and star $B$ with masses ${m_A}$ and ${m_B}$ revolving in a circular orbit of radii ${r_A}$ and ${r_B}$ respectively. If ${T_A}$ and ${T_B}$ are the time period of star $A$ and star $B$ respectively, then

The mass of the moon is about $1.2\%$ of the mass of the earth. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on earth

An artificial satellite of mass $m$ of a planet (radius $R$, mass ${M})$ revolves in a circular orbit whose orbital radius in $n$ times the radius of the planet. In the process of motion, the satellite experiences a slight resistance due to cosmic dust. Assuming the resistive force ${F}={kv}^2$, where ${k}$ is a constant and $v$ the instantaneous velocity. The time taken by the satellite to fall from its orbit to the surface of the planet is found $\frac{m}{k} \sqrt{\frac{R}{G m}}(y \sqrt{n}-1)$. Find $y$.

Assertion: Particle of mass $m$ dropped into a hole made along the diameter of the earth from one end to the other end executes simple harmonic motion.
Reason: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

I. The geo-stationary satellite always has circular orbit.
II. The time period of satellite depends on mass of the satellite, mass of the earth and height of satellite from the surface of earth.
Which of the following statement(s) is/are incorrect?

The ratio of acceleration due to gravity at a height $h$ above the surface of the earth and at a depth $h$ below the surface of the earth for $h < \; <$ radius of earth

A double star consists of two stars having masses $M$ and $2 M$. The distance between their centres is equal to $r$. They revolve under their mutual gravitational interaction. Then, which of the following statement(s) is/are correct?

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

Two satellites of mass 400 kg and 600 kg revolve around the earth is circular orbits of radii 10 R and 20 R respectively where R is the radius of the earth the speed of the two satellites will be in the ratio

The correct option is

Find the work done to take a particle of mass $\mathrm{m}$ from surface of the earth to a height equal to 2R

The diameters of two planets are in the ratio of $4: 1 \&$ mean density have ratio $1: 2$, then the ratio of $g$ on the planets will be