Gravitation practice · Medium

In a gravitational field, at a point where the gravitational potential is zero

Escape velocity when a body of mass $\mathrm{m}$ is thrown vertically from the surface of the earth is $\mathrm{v}$, what will be the escape velocity of another body of mass $4 \mathrm{~m}$ is thrown vertically

Assertion: A satellite can not be set on a stable orbit in a plane not passing through the earth's centre.
Reason: For the orbital motion of satellite, the centripetal force is provided by gravitational pull of earth on satellite.

Statement I: The weight of a body at the centre of earth is zero

Statement II: The mass of a body decreases with increase in depth below the surface of earth.

Which is constant for a satellite in orbit

If the total energy of a satellite is negative. It
means

The moon does not fall to Earth because:

In a certain region of space, the gravitational field is given by $-k/r$, where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = {r_0}$ be ${V_0}$, then what is the expression for the gravitational potential V?

Two bodies of masses $m$ and $M$ are placed a distance $d$ apart. The gravitational potential at the position where the gravitational field due to them is zero is $V$, then

The period of revolution of planet A around the sun is 8 times that $B$. The distance of a from the sun is how many times greater than that of $B$ from the sun?

Which of the following is always positive?

Two satellites ${S_1}$ and ${S_2}$ revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 4 hr and 6 hr respectively. The radius of the orbit of ${S_1}$ is 104 km. The angular speed of ${S_2}$ as observed by an astronaut in ${S_1}$ (in radius)

The mass and diameter of a planet have twice the value of the corresponding parameters of Earth. Acceleration due to gravity on the surface of the planet is:

Mark the correct statements.

I. Gravitational potential at the centre of curvature of a thin hemispherical shell of radius $R$ and mass $M$ is equal to $G M / R$

II. Gravitation field strength at a point lying on the axis at a distance of ' $a$ ' on a thin, uniform circular ring of radius $\mathrm{R}$ and mass $\mathrm{M}$ is equal $\frac{G M R}{\left(a^2+R^2\right)^{3 / 2}}$

III. Newton's law of gravitation for gravitational force between two bodies is applicable only when bodies have sphrical symmetric distribution of mass

Average density of the earth

The escape velocity of a body from the earth's surface is $v_e$. If the same body is projected from the surface of the earth with the velocity $2 v_e$, then the velocity of the body when it reaches to infinity, i.e., beyond the earth's gravitational field is

The value of g on the earth’s surface is $980\mathrm{\;cm}{\mathrm{s}^{ - 2}}$. Its value at a height of 64 km from the earth’s surface is

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

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.