Gravitation

If the density of earth is doubled keeping its radius constant then acceleration due to gravity will be (g=9.8 m/s²)

A satellite is launched into a circular orbit of radius R around earth while a second satellite is launched into an orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is

The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to

The ratio of radii of planets A and B is K₁ and ratio of accelerations due to gravity on them is K₂. The ratio of escape velocities from them will be

Two planets at mean distances d₁ and d₂ from the sun have their frequencies n₁ and n₂ respectively. Then

The kinetic energy needed to project a body of mass m from the surface of earth (radius R) to infinity is

Two satellites of 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 statements is true?

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 3 V, then the speed of satellite B will be

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

Two spheres of mass 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 be

A planet moving along an elliptical orbit is closest to the sun at a distance of 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 particle of masses 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

Weight of a body of mass m decreases by 1% when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

The depth at which the effective value of acceleration due to gravity is g/4 is (R=Radius of earth)

The height at which the weight of a body becomes 1/16 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 5 R above that surface of the earth, R being the radius of the earth. The time period of another satellite in hours at a height of 2 R from the surface of the earth is:

If vₑ is escape velocity and v₀ is orbital velocity of a satellite for orbit close to the earth’s surface, then these are related by:

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. If 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 3 R 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 acceleration due to gravity on the surface of earth)

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

The acceleration due to gravity becomes (g/2) where g=acceleration due to gravity on the surface of the earth at a height equal to

A planet in a distinct solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s⁻¹ the escape velocity from the surface of the planet would be

The weight of a body on surface of earth is 12.6 N. When it is raised to a height half the radius of earth its weight will be

If R is the radius of the earth and g is the acceleration due to gravity on the earth surface, the mean density of the earth is

The moon’s radius is 1/ 4 that of the earth and its mass is 1 / 80 times that of the earth.If g represents the acceleration due to gravity on the surface of the earth, then on the surface of the moon its value is

For a satellite escape velocity is 11 kms⁻¹.If the satellite is launched at an angle of 60° with the vertical, then escape velocity will be

Two bodies of masses m₁ and m₂ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity at a separation distance r between them is

The escape velocity from the earth’s surface is 11 kms⁻¹. A certain planet has a radius twice that of the earth but its mean density is the same as that of the earth. The value of the escape velocity from this planet would be

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

If r denotes the distance between sun and the earth, then the angular momentum of the earth around the sun is proportional to