An object is propelled vertically to a maximum height of 4R from the surface of a planet of radius R and mass M. The speed of object when it returns to the surface of the planet is -

A small body of mass is projected with a velocity just sufficient to make it reach from the surface of a planet ( or radius 2R and mass 3M ) to the surface of another planet (or radius R and mass M ). The distance between the centres of the two spherical planets is 6R . the distance of the body from the centre of bigger planet is 'x' at any moment. During the journey, find the distance 'x' where the speed of the body is (a) maximum (b) minimum. Assume motion of body along the line joining centres of planets.

Escape velocity of a body from the surface of a spherical planet of mass M, radius R and density p is

Derive an expression for the escape velocity of an object from the surface of a planet.

What will be the gravitational potential on the surface of a planet of mass M and radius R ?

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to 1/3rd the escape velocity for the planet. The maximum height attained by the body is

Escape speed on the surface of a planet varies with the mass m of a body as

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is