Gravitation practice · Medium

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?

Assertion: The time period of revolution of a satellite around a planet is directly proportional to the radius of the orbit of the satellite.

Reason: Artificial satellite do not follow Kepler's laws of planetary motion.

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

Find the distance of a point from the earth's centre where the resultant gravitational field due to the earth and the moon is zero. The mass of the earth is $6.0 \times 10^{24} \mathrm{~kg}$ and that of the moon is $7.4 \times 10^{22} \mathrm{~kg}$. The distance between the earth and the moon is $4.0 \times 10^5 \mathrm{~km}$.

If a body of mass $m$ has to be taken from the surface of the earth to a height $h=4 R$, then the amount of energy required is ($R=$ radius of the earth)

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $V.$ Due to the rotation of the planet about its axis the acceleration due to gravity ${g}$ at equator is 1/2 of $g$ at poles. The escape velocity of a particle on the planet in terms of ${V}$ from the pole of the planet is

The weight of an astronaut, in an artificial satellite revolving around the earth, is

An earth's satellite makes a circle around the earth in 90 minutes. Calculate the height of the satellite above the earth's surface. Given radius of the earth is $6400 \mathrm{~km}$ and $g=980 \mathrm{~cms}^{-2}$.

A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reached the centre of the earth is (Given: gravitational potential at the centre of earth $= - \frac{3}{2}\,\left( {\frac{{GM}}{R}} \right)$)

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)

Two satellites A and B have masses m and 2m respectively. A is in a circular orbit of radius R and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, ${T_A}/{T_B}$ is

A satellite is orbiting just above the surface of the earth with period $T$. If $d$ is the density of the earth and $G$ is the universal constant of gravitation, the quantity $\frac{3 \pi}{G d}$ represents

Hubble's law is related with

An artificial satellite is moving in a circular orbit (of radius $r$) around the earth and its orbital speed is equal to $\frac{1}{3}{\text{rd}}$ of the escape speed from the earth’s surface. The value of $r$ in terms of radius of earth $R$ is

Which pair of PE and KE is possible for a polar satellite? [Assume PE=0 at infinity]

Consider Earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The gravitational field measured by:

If satellite is shifted towards the earth. Then time period of satellite will be

For a satellite escape velocity is $11 \mathrm{~km} / \mathrm{s}$. If the satellite is launched at angle of $60^{\circ}$ with the vertical, then escape velocity will be

If the distance between the sun and the earth is increased by three times, then attraction between two will

If ${g_e},\;{g_h}\,and\,{g_d}$ be the accelerations due to gravity at earth’s surface, a height $h$ and at depth $d$ respectively. Then

In case of an orbiting satellite, if the radius of orbit is decreased,

If the escape velocity on the earth is 11.2 Km/s, its value for a planet having double the radius and 8 times the mass of the earth is …… (in km/s)

A body weighs $90 \mathrm{~kgf}$ on the surface of the earth. How much will it weigh on the surface of Mars whose mass is $1 / 9$ and the radius is $1 / 2$ of that of the earth?

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

When a satellite moves around the earth in a
certain orbit, then the quantity that remains
constant is

A planet is orbiting the sun in an elliptical orbit. Let $U$ denote the potential energy and $K$ denote the kinetic energy of the planet at an arbitrary point on the orbit. Choose the correct statement.

Assertion: Average density of the earth depends on the value of $g$.

Reason: It is because, the density is the ratio of the mass of the earth to its volume.

Two point masses of mass $4m$ and $m$ respectively separated by distance $d$ are revolving under mutual force of attraction. Ratio of their kinetic energies will be

If the earth stops rotating about its axis, then the magnitude of gravity

A remote sensing satellite of the earth revolves in a circular orbit at a height of $250 \mathrm{~km}$ above the earth's surface. What is the period of revolution of the satellite? Radius of the earth, $R=6.38 \times 10^6 \mathrm{~m}$, and acceleration due to gravity on the surface of the earth, $g=9.8 \mathrm{~ms}^{-2}$.