Gravitation

A simple pendulum has a periodic time ' $\mathrm{T}_1$ ' when it is on the surface of earth of radius ' $R$ '. Its periodic time is ' $\mathrm{T}_2$ ' when it is taken to a height ' $R$ ' above the earth's surface. The value of $\frac{T_2}{...

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as at present weight is ( $\mathrm{g}=$ gravitational acceleration, $\mathrm{R}=$ equatorial radius of t...

A satellite is orbiting just above the surface of the planet of density ' $\rho$ ' with periodic time ' $T$ '. The quantity $\mathrm{T}^2 \rho$ is equal to ( $\mathrm{G}=$ universal gravitational constant)

A boy weighs 72 N on the surface of earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relation...

A satellite of mass ' $m$ ' is revolving around the earth of mass ' $M$ ' in an orbit of radius ' $r$ ' with constant angular velocity ' $\omega$ '. The angular momentum of satellite is
( $\mathrm{G}=$ Universal constant of gravitation)

The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ is

The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If $R$ is the radius of earth, then radius of the planet would be

Assuming that the earth is revolving around the sun in circular orbit of radius R , the angular momentum is directly proportional to $\mathrm{R}^{\mathrm{n}}$. The value of ' $n$ ' is

The depth 'd' at which the value of acceleration due to gravity becomes $\frac{1}{n-1}$ times the value at the earth's surface is ($R=$ radius of the earth)

The acceleration due to gravity at the surface of the planet is same as that at the surface of the earth, but the density of planet is thrice that of the earth. If 'R' is the radius of the earth, the radius of the planet will be

For a satellite moving in an orbit around the earth at height ' $h$ ' the ratio of kinetic energy to potential energy is

A body is projected in vertically upward direction from the surface of the earth of radius ' $R$ ' into space with velocity ' $n V_{\mathrm{e}}$ ' $(\mathrm{n}<1)$. The maximum height from the surface of earth to which a body can reach is

The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth to the escape velocity at a planet is

A small planet is revolving around a very massive star in a circular orbit of radius ' $R$ ' with a period of revolution ' $T$ '. If the gravitational force between the planet and the star were proportional to '$R^{-5 / 2}$', then '$T$' wou...

A body starts from rest from a distance $\mathrm{R}_0$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ( $R=$ radius of earth, $M=$ mass of earth)

The height ' h ' from the surface of the earth at which the value of ' $g$ ' will be reduced by $64 \%$ than the value at surface of the earth is ( $\mathrm{R}=$ radius of the earth)

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '\(3 \mathrm{R}\)' from the earth's surface. The time period of the pendulum will be ( \(R=\) radius of earth)

A body weighs \(300 \mathrm{~N}\) on the surface of the earth. How much will it weigh at a distance \(\frac{R}{2}\) below the surface of earth? ( \(R \rightarrow\) Radius of earth)

A thin rod of length '\(L\)' is bent in the form of a circle. Its mass is '\(M\)'. What force will act on mass '\(m\)' placed at the centre of this circle?
( \(\mathrm{G}=\) constant of gravitation)

Consider a planet whose density is same as that of the earth but whose radius is three times the radius '\(R\)' of the earth. The acceleration due to gravity '\(\mathrm{g}_{\mathrm{n}}\)' on the surface of planet is $$\mathrm{g}_{\mathrm{n}...

Periodic time of a satellite revolving above the earth's surface at a height equal to radius of the earth '\(R\)' is [ \(g=\) acceleration due to gravity]

The value of acceleration due to gravity at a depth '\(d\)' from the surface of earth and at an altitude '\(h\)' from the surface of earth are in the ratio

Considering earth to be a sphere of radius '\(R\)' having uniform density '\(\rho\)', then value of acceleration due to gravity '\(g\)' in terms of \(R, \rho\) and \(\mathrm{G}\) is

A body (mass \(\mathrm{m}\) ) starts its motion from rest from a point distant \(R_0\left(R_0>R\right)\) from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( \(\mathrm{G}=\) universa...

Earth is assumed to be a sphere of radius R. If '\(\mathrm{g}_\phi\)' is value of effective acceleration due to gravity at latitude \(30^{\circ}\) and '\(g\)' is the value at equator, then the value of \(\left|g-g_\phi\right|\) is ($$\omega...

If two identical spherical bodies of same material and dimensions are kept in contact, the gravitational force between them is proportional to \(\mathrm{R}^{\mathrm{X}}\), where \(\mathrm{x}\) is non zero integer [Given : \(\mathrm{R}\) is ...

A body of mass '\(\mathrm{m}\)' is raised through a height above the earth's surface so that the increase in potential energy is \(\frac{\mathrm{mgR}}{5}\). The height to which the body is raised is ( \(\mathrm{R}=\) radius of earth, $$\mat...

A mine is located at depth \(R / 3\) below earth's surface. The acceleration due to gravity at that depth in mine is (\(R=\) radius of earth, \(g=\) acceleration due to gravity)

If two planets have their radii in the ratio \(x: y\) and densities in the ratio \(m: n\), then the acceleration due to gravity on them are in the ratio

Consider a light planet revolving around a massive star in a circular orbit of radius '\(r\)' with time period '\(T\)'. If the gravitational force of attraction between the planet and the star is proportional to \(\mathrm{r}^{\frac{7}{2}}\)...

The height at which the weight of the body becomes \(\left(\frac{1}{9}\right)^{\text {th }}\) its weight on the surface of earth is \((\mathrm{R}=\) radius of earth)

Time period of simple pendulum on earth's surface is '\(\mathrm{T}\)'. Its time period becomes '\(\mathrm{xT}\)' when taken to a height \(\mathrm{R}\) (equal to earth's radius) above the earth's surface. Then the value of '\(x\)' will be

The depth at which acceleration due to gravity becomes \(\frac{\mathrm{g}}{2 \mathrm{n}}\) is \((\mathrm{R}=\) radius of earth, \(\mathrm{g}=\) acceleration due to gravity on earth's surface, \(\mathrm{n}\) is integer)

A simple pendulum is oscillating with frequency '\(F\)' on the surface of the earth. It is taken to a depth \(\frac{\mathrm{R}}{3}\) below the surface of earth. ( \(\mathrm{R}=\) radius of earth). The frequency of oscillation at depth $$\ma...

A body is projected vertically upwards from earth's surface of radius '\(R\)' with velocity equal to \(\frac{1^{\text {rd }}}{3}\) of escape velocity. The maximum height reached by the body is

A body of mass '\(\mathrm{m}\)' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '\(R\)' above the surface of the earth of radius '\(R\)' and Mass '\(M\)', then its kinetic energy is

The radius of earth is \(6400 \mathrm{~km}\) and acceleration due to gravity \(\mathrm{g}=10 \mathrm{~ms}^{-2}\). For the weight of body of mass \(5 \mathrm{~kg}\) to be zero on equator, rotational velocity of the earth must be (in $$\mathr...

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

The radius of the orbit of a geostationary satellite is (mean radius of earth is '\(R\)', angular velocity about own axis is '\(\omega\)' and acceleration due to gravity on earth's surface is '\(g\)')

For a satellite orbiting around the earth in a circular orbit, the ratio of potential energy to kinetic energy at same height is

There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period of oscillation of second's pendulum on the planet will be

A satellite moves in a stable circular orbit round the earth if (where \(\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}}\) and \(\mathrm{V}_{\mathrm{e}}\) are the horizontal velocity, critical velocity and escape velocity respectively)

A system consists of three particles each of mass '\(m_1\)' placed at the corners of an equilateral triangle of side '\(\frac{\mathrm{L}}{3}\)', A particle of mass '\(\mathrm{m}_2\)' is placed at the mid point of any one side of the triangl...

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( \(R\) = radius of earth)

The masses and radii of the moon and the earth are \(\mathrm{M_1, R_1}\) and \(\mathrm{M_2, R_2}\) respectively. Their centres are at a distance \(\mathrm{d}\) apart. What should be the minimum speed with which a body of mass '\(m\)' should...

A body weighs \(500 \mathrm{~N}\) on the surface of the earth. At what distance below the surface of the earth it weighs \(250 \mathrm{~N}\) ? (Radius of earth, \(\mathrm{R}=6400 \mathrm{~km}\) )

The period of revolution of planet \(\mathrm{A}\) around the sun is 8 times that of planet \(\mathrm{B}\). How many times the distance of A from the sun is greater than that of B from the sun?

If the horizontal velocity given to a satellite is greater than critical velocity but less than the escape velocity at the height, then the satellite will

Three point masses, each of mass 'm' are kept at the corners of an equilateral triangle of side 'L'. The system rotates about the centre of the triangle without any change in the separation of masses during rotation. The period of rotation ...