Gravitation

A meteor of mass ' $m$ ' having a speed ' $V$ ' at infinity reaches the surface of the Earth with a speed of ( $v_c$ is escape speed from the Earth's surface)

Which of the following is incorrect about the gravitational force between two bodies?

The force of mutual attraction between any two objects by virtue of their masses is

A body is projected from the Earth's surface with a speed $\sqrt{5}$ times the escape speed $\left(V_e\right)$. The speed of the body when it escapes from the gravitational influence of the Earth is

If the orbital speed of a body revolving in a circular path near the surface of the Earth is $8 \mathrm{kms}^{-1}$, then the orbital speed of a body revolving around the Earth in a circular orbit at height of $19,200 \mathrm{~km}$ from the ...

If a body is projected vertically from the surface of the Earth with a speed of $8000 \mathrm{~ms}^{-1}$, then the maximum height reached by the body is
(Radius of the Earth $=6400 \mathrm{~km}$ and acceleration due to gravity $=10 \mathrm{...

The ratio of the time periods of a simple pendulum at heights $2 R_E$ and $3 R_E$ from the surface of the Earth is ( $R_E$ is radius of the Earth)

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth is

Regarding fundamental forces in nature, the correct statement is

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is
(Radius of the earth $=6400 \mathrm{~km}$ )

The range of gravitational forces is

An object of mass $m$ at a distance of $20 R$ from the centre of a planet of mass $M$ and radius $R$ has an initity velocity $u$. The velocity with which the object hits the surface of the planet is( $G$-Universal gravitational constant)

Two stars of masses $M$ and $2 M$ that are at a distance $d$ apart, are revolving one around another. The angular velocity of the system of two stars is ( $G$-Universal gravitational constant)

The ratio of the radii of a planet and the earth is $1: 2$, the ratio of their mean densities is $4: 1$. If the acceleration due to gravity on the surface of the earth is $9.8 \mathrm{~ms}^{-2}$, then the acceleration due to gravity on the ...

A body of mass $m$ is at height $R$ from the surface of the earth where $R$ is the radius of the earth. If the body is taken from here to a height of $3 R$ from the surface of the earth, the increase in the gravitational potential energy of...

Gravitational forces operate among which of the following?

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $3 r / 2$ is

The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface of the same planet is

A ring has a mass $M$ and radius $R$. The distance of the point on its geometric axis from its centre at which the gravitational field is strongest is

The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then the ratio of the escape velocities from the planets is

Let the escape speed of an object on the earth's surface be $v_0$. The object is projected out with speed $5 v_0$. The speed of the object far away from the earth will be

Statement I The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is always positive.
Statement II The force of attraction between a hollow spherical shell of uniform density and a poi...

A uniform sphere $A$ with radius $R$ exerts a force $F$ on a small particle $B$ situated at a distance $2 R$ from the centre of the sphere. A spherical portion of diameter $R$ is cut from the sphere $A$ as shown in the figure. If $F^{\prime...

Four particles each of mass $m$ are placed at four vertices of a rectangle having side length as $3 l_0$ and $4 l_0$. The potential energy of the system in $\frac{G m^2}{l_0}$ is

Three particles, each of mass $M$, situated at the vertices of an equilateral triangle of side length $l$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle whi...

A rocket is fired vertically with a speed of $4 \mathrm{~km} / \mathrm{s}$ from the earth's surface. How far from the earth does the rocket go before returning to the earth?
(Take, radius of earth $=6.4 \times 10^6 \mathrm{~m}$ and $g=10 \m...

If the escape velocity on earth is $11.2 \mathrm{~km} / \mathrm{s}$, its value for a planet having double the radius and 8 time the mass of earth is

A mass $M$ is split into two parts $m_0$ and $M-m_0$. These two masses are then separated by a distance $D$. If the gravitational force between the parts is maximum, then the ratio $\frac{m_0}{M}$ is

A planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun
(i) is zero in no part of the motion.
(ii) is zero in some parts of the orbit.
(iii) is zero in one complete revolut...

If the radius of the earth shrinks by $1 \%$, its mass remaining the same, then the acceleration due to gravity on the earth surface would

The long range force experienced by a neutral particle with a finite mass

Choose the correct statement.

The graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance from the centre of the earth (radius of the earth $=R_e$ ) is