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

At what height from the surface of earth the gravitation potential and the value of g are -5.4 × 10⁷ J kg^-2 and 6.0 ms^-2 respectively? Take, the radius of earth as 6400 km.

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

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

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

Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between the sun and planet

i.e. T² = Kr³, 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 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 centers equal to 12 R. If they attract each other due to gravitational force only,then the distance covered by the smaller body before collision is

A remote sensing satellite of earth revolves in a circular orbit at a height of 0.25 × 10⁶ m above the surface of earth. If earth's radius is 6.38 × 10⁶ m and g = 9.8 ms^-2,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 = 5.98 × 10²⁴ kg) have to be compressed to be a black hole?

Dependence of intensity of gravitational filed (E) of the earth with distance (r) from center of the earth is correctly represented by

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

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

A spherical planet has a mass M_p and diameter D_p. 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 earth at a height of 5 R above that surface of the earth, R being the radius of the earth. The time period of another satellite in how at a height of 2 R from the surface of the earth is

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 v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁ /v₂ 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

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

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

The figure shows elliptical orbit of a planet m about the sun S.The shaded area SCD is twice the shaded area SAB. If t₁ is the time for the planet to move from C to D and t₂ is the time to move from A to B, then

A roller coaster is designed such that riders experience

" weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

Two satellite of the earth, S₁ and S₂ are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which one of the following statement is true?

The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is ƒv_e, where v_eis its escape velocity from the surface of the earth. The value of ƒ is

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

Imagine a new planet having the same density as that of the earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of the earth is g and that on the surface of the new planet is g', then

That density of newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth R, the radius of the planet would be

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on the planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?

A body of mass m is placed on the earth's surface. It is then from the earth's surface to a height h = 3 R, then the change in gravitational potential energy is

A body attains a height equal to the radius of the earth. The velocity of the body with which it was projected is

Escape velocity from the earth is 11.2 km/s. Another planet of same mass has radius 1/4 times that of the earth. What is the escape velocity from another planet ?

The escape velocity of a sphere of mass m is given by (G = universal gravitational constant, M_e = mass of the earth and R_e = radius of the earth)

A rubber ball is dropped from a height of 5 m on a planet where the acceleration due to gravity is not known. On bouncing it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of

The period of revolution of the planet A round the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun?

The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

A ball is dropped from a satellite revolving around the earth at a height of 120 km.The ball will

What will be the formula of the mass in terms of g, R and G? (R = radius of the earth)

The escape velocity from the surface of the earth v_e . The escape velocity from the surface of a planet whose mass and radius are three times those of the earth, will be

A satellite A of mass m is at a distance r from the surface of the earth. Another satellite B of mass 2 m is at a distance of 2 r are in the ratio of

The escape velocity from the earth is 11.2 km/s/ if a body is to be projected in a direction making an angle 45° to the vertical, then the escape velocity is

The mean radius of the earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at the earth's surface is g. What will be the radius of the orbit of a geostationary satellite?

The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?

A second pendulum is mounted in a rocket. It period of oscillation decreases when the rocket

A planet is moving in an elliptical orbit around the sun. If T,U,E and L stand for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the center of force, which of the following is correct?

If the gravitational force between two objects were proportional to 1 / R(and not as 1/R²), wherer R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

For a satellite escape veocity is 11 km/s. If the satellite launched at an angle of 60° with the vertical, then escape velocity will be

The distance of two planets from the sun are 10¹³ and 10¹² m respectively. The ratio of time periods of these two planets is

The largest and the shortest distance of the earth from the sun are r₁ and r₂. Its distance from the sun when it is perpendicular to the major axis of the orbit drawn from the sun