The orbital velocity of a planet revolving close to earth's surface is 

If the gravitational force between two objects were proportional to 1/R (and not as $1/R^2$) where R is the separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to:

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 

Which of the following quantities does not depend upon the orbital radius of the satellite ?

A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is -

A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon’s orbit. The satellite completes one revolution in

If the acceleration due to gravity at a height 1km above the earth is similar to a depth d below the surface of the earth, then: 

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

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 $-5.4\times {10}^{7}J k{g}^{-2}$ and $6.0 m{s}^{-2}$ respectively? (Take, the radius of earth as 6400 km.)

Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. T²=Kr^3, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is F=GMm/r², here G is gravitational constant. The relation between G and K is described as
 

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

(1)2.5 R

(2)4.5 R

(3)7.5 R

(4)1.5 R

A remote sensing satellite of the earth revolves in a circular orbit at a height of 0.25 x 10⁶ m above the surface of the earth. If the earth’s radius is 6.38x10⁶ m and g=9.8ms^-1, then the orbital speed of the satellite is

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

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=5.98X 10²⁴ kg) have to be compressed to be a black hole?

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

(a) (b) (c) (d)

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 the body will be
\(1.~2mgR\)
\(2.~\frac{2}{3}mgR\)
\(3.~3mgR\)
\(4.~\frac{1}{3}mgR\)
 

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m,  4m, 8m, 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 1/16th, its weight on the surface of the earth (radius R), is:

A planet moving along an elliptical orbit is closest to the sun at a distance ${\mathrm{r}}_1$ and farthest away at a distance of ${\mathrm{r}}_2$. If ${\mathrm{v}}_1 \mathrm{and} {\mathrm{v}}_2$ are the linear velocities at these points respectively, then the ratio $\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}$ is:

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest:

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 earth. The minimum value of u so that the particle does not return back to earth is

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 speed of satellite B will be

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

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius ${\mathrm{R}}_1$ to another of radius ${\mathrm{R}}_2({\mathrm{R}}_2>{\mathrm{R}}_1)$ is

The dependence of acceleration due to gravity g on the distance r from the centre of the earth assumed to be a sphere of radius R of uniform density is as shown in the figure below -

                          (1)                                                           (2)

The correct figure is

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If $t_1$ is the time for planet to move from C to D and $t_2$ is the time to move from A to B, then

Mass and radius of the earth is M and R respectively, then the gravitational potential at a distance R/3 from the centre of the earth is

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

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 statement is not correct?