Gravitation practice · Mixed difficulty

A geostationary satellite is orbiting around an arbitrary planet $P$ at a height of $11R$ above the surface of $P$, $R$ being the radius of $P$. The time period of another satellite in hours at a height of $2R$ from the surface of $P$ is……
$P$ has the time period of 24 h.

A body is moving in a low circular orbit about a planet of mass $M$ and radius$R$. The radius of the orbit can be taken to be $R$ itself. Then, the ratio of the speed of this body in the orbit to the escape velocity from the planet is

When a satellite going round the earth in a circular orbit of radius $r$ and speed $v$ loses some of its energy, then $r$ and $v$ change as

A planet is moving in an elliptical orbit around the sun. If $T$, $\mathrm{V}, \mathrm{E}$ and $\mathrm{L}$ stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, then which of the following is correct?

What effect occurs on the frequency of a pendulum of it is taken from the earth surface to deep into a mine?

The radius of earth is R. Height of a point vertically above the earth's surface at which acceleration due to gravity becomes 1% of its value of the surface is

Four particles of masses $m, 2 m, 3 m$ and $4 m$ are kept in sequence at the corners of a square of side $a$. The magnitude of gravitational force acting on a particle of mass $\mathrm{m}$ placed at the centre of the square will be

A satellite of mass m is moving around the earth in a circular orbit of radius r. If the mass of the earth is M, the energy required to take the satellite to an orbit of radius 3r is

A man weighs $80 \mathrm{kg}$ on the surface of the earth. His weight on a geostationary satellite is

Gravitational field due to a solid sphere

A particle of mass $m$ is dropped from a great height $h$ above the hole in the earth dug along its diameter. Then, which of the following statement is correct?

The orbit of geostationary satellite is circular, the time period of satellite depends on
(i) mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of earth
Which of the following correct?

When a satellite is shifted from a nearer orbit to a farther orbit, its

(a) Gravitational potential energy increases

(b) Kinetic energy increases

(c) Gravitational potential energy decreases

(d) Kinetic energy decreases

Choose the correct option.

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.

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 $g=980 \mathrm{~cms}^{-2}$.

On which quantity the escape velocity for earth does not depend on

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 $= - \frac{3}{2}\,\left( {\frac{{GM}}{R}} \right)$)

When we move from equator to pole, the value of acceleration due to gravity(g)

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

When the radius and mass of earth are increased by $0.5 \%$. Which of the following statement is correct at the surface of the earth?

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