Gravitation

In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius $R$ is proportional to:

Two planets $P_1$ and $P_2$ with equal mass have radii $R_1$ and $R_2$, respectively, where $R_2=\frac{R_1}{2}$. The escape speeds of $P_1$ and $P_2$ are $v_1$ and $v_2$, respectively. Then $\frac{v_2}{v_1}$ is:

The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to the radius of the Earth ' $R$ ' will be

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

An object of mass \(100 \mathrm{~kg}\) falls from point \(A\) to \(B\) as shown in figure. The change in its weight, corrected to the nearest integer is (\(R_E\) is the radius of the earth)

The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2 R\) from the surface of the earth is:

The mass of a planet is \(\frac{1}{10}\)th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

If \(\mathrm{R}\) is the radius of the earth and \(\mathrm{g}\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be :

The escape velocity of a body on the earth surface is \(11.2 \mathrm{~km} / \mathrm{s}\). If the same body is projected upward with velocity \(22.4 \mathrm{~km} / \mathrm{s}\), the velocity of this body at infinite distance from the centre ...

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 :

Two bodies of mass \(m\) and \(9 m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (\(G=\) gravitational constant) :

In a gravitational field, the gravitational potential is given by, \(V = - {K \over x}\) (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If W1, W2 and W3 represent the work done by the gravitational force along the respective paths, then :

Match List - I with List - II

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A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

A particle of mass 'm' is projected with a velocity \(\upsilon\) = kVe = (k < 1) from the surface of the earth. (Ve = escape velocity)The maximum height above the surface reached by the particle is :

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

A body weight 200 N on the surface of earth. How much will it weight half way down to the centre of the earth?

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

If the mass of the Sun were ten times smaller
and the universal gravitational constant were
ten times larger in magnitude, which of the
following is not correct?

The kinetic energies of
a planet in an elliptical
orbit about the Sun, at
positions A, B and C are
KA, KB and KC, respectively. AC is the major
axis and SB is perpendicular to AC at the position
of the Sun S as shown in the figure. Then

The acceleration due to gravity at a height at a height 1 km above the rearth is the same as at a depth d below the surface of earth. Then

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is

Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by

At what height from the surface of earth the gravitation potential and the value of g are \(-\)5.4 \(\times\) 107 J kg\(-\)1 and 6.0 m s\(-\)2 respectively? Take the radius of earth as 6400 km.

The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is

Kepler's third law states that square of period of revoluation (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here K is constant. If the masses of sun and planet are...

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 \(\times\) 106 m above the surface of earth. If earth's radius is 6.38 \(\times\) 106 m and g = 9.8 ms\(-\)2, then the orbital speed of the satellite i...

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 \(\times\) 1024 kg) have to be compressed to be a black hole?

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. VP and VE are escape velocities of the planet and the earth, respectively, then

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

A body of mass 'm' is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, . . . , respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

The height at which the weight of a body becomes \({\left( {{1 \over {16}}} \right)^{th}}\), its weight on the surface of earth (radius R), is

A spherical planet has a mass MP and diameter DP. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of the earth is

Which one of the following plots represents the variation of gravitiational field on a particle with distance r due to a thin spherical shell of radius R? (r is measured from the centre of the spherical shell)

If \({v_e}\) is escape velocity and \({v_o}\) is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

A planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If \(v\)1 and \(v\)2 are the linear velocities at these points respectively, then the ratio \({{{v_1}} \over {{v_2}}}\) ...

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :

A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the...

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3V, then the speed of satellite B will be

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be

A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :