Gravitation

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

The depth from the surface of the earth of radius \(\mathrm{R}\), at which acceleration due to gravity will be \(60 \%\) of the value on the earth surface is

The average density of the earth is [g is acceleration due to gravity]

The radius of a planet is twice the radius of the earth. Both have almost equal average mass densities. If '\(V_P\)' and '\(V_E\)' are escape velocities of the planet and the earth respectively, then

The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How much work is done is lifting a body of mass 5 kg through a distance of 2 m on the planet ? (g = 10 ms\(^{-2}\))

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite will satellite is increased to four times the previous value, the new time period of the satellite will be

A body of mass 'M' and radius 'R', situated on the surface of the earth becomes weightless at its equator when the rotational kinetic energy of the earth reaches a critical value 'K'. The value of 'K' is given by [Assume the earth as a soli...

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is '\(V_e\)', then the escape velocity from the planet is

Two satellites of same mass are launched in circular orbits at heights '\(R\)' and '\(2 R\)' above the surface of the earth. The ratio of their kinetic energies is (\(R=\) radius of the earth)

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

A particle of mass '\(m\)' is kept at rest at a height \(3 R\) from the surface of earth, where '\(R\)' is radius of earth and '\(M\)' is the mass of earth. The minimum speed with which it should be projected, so that it does not return bac...

When the value of acceleration due to gravity '\(g\)' becomes \(\frac{g}{3}\) above surface of height '\(h\)' then relation between '\(h\)' and '\(R\)' is
( \(\mathrm{R}=\) radius of earth)

A pendulum is oscillating with frequency '\(n\)' on the surface of the earth. It is taken to a depth \(\frac{R}{2}\) below the surface of earth. New frequency of oscillation at depth \(\frac{R}{2}\) is
[ \(R\) is the radius of earth]

The ratio of energy required to raise a satellite of mass '\(m\)' to height '\(h\)' above the earth's surface to that required to put it into the orbit at same height is [ \(\mathrm{R}=\) radius of earth]

For a body of mass '\(m\)', the acceleration due to gravity at a distance '\(R\)' from the surface of the earth is \(\left(\frac{g}{4}\right)\). Its value at a distance \(\left(\frac{R}{2}\right)\) from the surface of the earth is ( \(R=\) ...

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is

The depth 'd' below the surface of the earth where the value of acceleration due to gravity becomes \(\left(\frac{1}{n}\right)\) times the value at the surface of the earth is \((R=\) radius of the earth)

The depth at which acceleration due to gravity becomes \(\frac{\mathrm{g}}{\mathrm{n}}\) is [ \(\mathrm{R}\) = radius of earth, \(\mathrm{g}=\) acceleration due to gravity, \(\mathrm{n}=\) integer \(]\)

A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape the gravitational pull?

Earth has mass $M_1$ and radius $R_1$. Moon has mass $M_2$ and radius $R_2$. Distance between their centre is $r$. A body of mass $M$ is placed on the line joining them at a distance $\frac{r}{3}$ from centre of the earth. To project the ma...

The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will (v$_e$ = escape velocity of a body from the earth's surface)

A body is thrown from the surface of the earth velocity \(\mathrm{v} / \mathrm{s}\). The maximum height above the earth's surface upto which it will reach is (\(R=\) radius of earth, \(g=\) acceleration due to gravity)

The mass of earth is 81 times the mass of the moon and the distance between their centres is \(R\). The distance from the centre of the earth, where gravitational force will be zero is

The ratio of energy required to raise a satellite of mass \(m\) to a height \(h\) above the earth's surface of that required to put it into the orbit at same height is [\(R=\) radius of the earth]

As we go from the equator of the earth to pole of the earth, the value of acceleration due to gravity

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote radius and mass of the earth. If $\omega$ is the angular velocity of rotation of the earth about its own axis, then the tension on the string will ...

A hole is drilled half way to the centre of the earth. A body weighs 300 N on the surface of the earth. How much will, it weigh at the bottom of the hole?

 If $W_1, W_2$ and $W_3$ represent the work done in moving a particle from $A$ to $B$ along three different paths 1,2 and 3 (as shown in fig) in the gravitational field of the point mass ' $m$ '. Find the correct relation between ' $W_1$ ',...

The kinetic energy of a revolving satellite (mass $m$ ) at a height equal to thrice the radius of the earth $(R)$ is

A body is projected vertically from the surface of the earth of radius ' $R$ ' with velocity equal to half of the escape velocity. The maximum height reached by the body is

The radius of the earth and the radius of orbit around the sun are 6371 km and $149 \times 10^6 \mathrm{~km}$ respectively. The order of magnitude of the diameter of the orbit is greater than that of earth by

What is the minimum energy required to launch a satellite of mass ' $m$ ' from the surface of the earth of mass ' $M$ ' and radius ' $R$ ' at an altitude $2 R$ ?