Gravitation practice · Medium

A satellite is revolving around the earth at a height $h$. The satellite explodes into two equal parts, one part has zero velocity after the explosion, and the other moves in the same direction with double the orbital speed of the original satellite. The maximum height reached by the part with double the velocity is (Neglect the gravitational effects between the fragments)

Time speed of revolution of a nearest satellite around a planet of radius R is T. Period of revolution around another planet, whose radius is 3R but having same density is

Hubble's law is related with

According to Kepler, the period of revolution of a planet ($T$) and its mean distance from the sun ($r$) are related by the equation

Statement I: If ice on the pole melts, length of the day will shorten.

Statement II: Ice will flow towards equator and will result in the decrease in moment of inertia of earth resulting in decrease in frequency of rotation of earth.

(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.

For elliptical orbits, in the equation $T^2=\left(\frac{4 \pi^2}{{GM}_s}\right) R^3, R$ refers to

Given that centripetal force $F = - k/{r^2}$. The total energy is

Given below are two statements:

Statement I: If $E$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $E$.


In the light of the above statements, choose the most appropriate answer from the options given below

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

Assertion: Angular speed of a planet around the sun increases, when it is closer to the sun.

Reason: Total angular momentum of the system remains constant.

A planet revolving in elliptical orbit has
I. a constant velocity of revolution
II. has the least velocity when it is nearest to the sun
III. its areal velocity is directly proportional to its velocity.
IV. areal velocity is inversely proportional to its velocity.
V. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below.

Energy required to move an Earth’s satellite of mass m from an orbit of radius R to 5R is (M = mass of earth, R = radius of earth)

Two particles of equal masses are revolving in circular paths of radii ${r_1}\,and\,{r_2}$ respectively with the same speed. The ratio of their centripetal forces is

A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be

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

The mass of the moon is $\frac{1}{8}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

Two identical trains $P$ and $Q$ move with equal speeds on parallel tracks along the equator. $P$ moves from east to west and $Q$ from west to east

Acceleration due to gravity is maximum at (R is the radius of earth)

A pallet of mass 1 g is moving with an angular velocity of 1 $\mathrm{rads}{\mathrm{\;}^{ - 1}}$ along a circle of radius 1 m the centrifugal force is

A rocket is intended to leave the Earth’s gravitational field. The
fuel in its main engine is a little less than the amount that is
necessary and an auxiliary engine, (only capable of operating
for a short time) has to be used as well. When is it best to switch
on: the auxiliary engine?

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole

At what height from the surface of earth the total energy of a satellite is equal to its potential energy at a height of 2R from surface of earth…. (R = Radius of earth)

If gravitational constant is decreasing with time, what will remain unchanged in case of a satellite orbiting around earth

Assertion: The time period of a pendulum, on a satellite orbiting the earth is infinity.
Reason: Time period of a pendulum is inversly proportional to $\sqrt{g}$

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)

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

The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}\,and\,{W_3}$ respectively, then

A double star system consists of two stars A and B which have time period ${T_A}\;\mathrm{and\;}{\mathrm{T}_\mathrm{B}}$. Radius ${R_A}\;\mathrm{and\;}{R_B}$ and mass ${M_A}\;\mathrm{and\;}{M_B}$. Choose the correct option.

A person sitting on a chair in a satellite feels weightless because