If a planet of given density were made larger, its force of attraction for an object on its surface would increase because of the greater distance from the object to the centre of the planet. Which effect predominates?

A spherical hollow is made in a lead sphere of radius R such that its surface touches the outside surface of the lead sphere and passes through the centre. The mass of the lead sphere before hollowing was M . The force of attraction that this sphere would exert on a particle of mass m which lies at a distance d from the centre joining the centre of the sphere and the hollow is

If the angular velocity of a planet about its own axis is halved, the distance of geostationary satellite of this planet from the centre of the centre of the planet will become

The escape velocity of an object projected from the surface of a given planet is independent of

The planet Egabbac (in another solar system) has a radius twice that of the earth's but an average mass density which is the same as the earth. Would the weight of an object on Egabbac's surface to be the same as on the earth's greater than on the earth's or less than on the earth's ? If greater or less than on the earth's then by how much?

Statement I: In free space a uniform spherical planet of mass M has a smooth narrow tunnel along its diameter. This planet and another superdense small particle of mass M start approaching towards each other from rest under action of their gravitational forces. When the particle passes through the centre of the planet, sum of kinetic energies of both the bodies is maximum. Statement II: When the resultant of all forces acting on a particle or a particle like object (initially at rest) is constant in direction, the kinetic energy of the particle keeps on increasing.

If the radius of a planet is R and its density is rho , the escape velocity from its surface will be