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.

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

If v_(e) is the escape velocity of a body from a planet of mass 'M' and radius 'R . Then the velocity of the satellite revolving at height 'h' from the surface of the planet will be

An object is projected vertically upward from the surface of the earth of mass M with a velocity such that the maximum height reached is eight times the radius R of the earth. Calculate: (i) the initial speed of projection (ii) the speed at half the maximum height.

The ratio of acceleration due to gravity at depth 'R' from the surface of planet and at height ' r' from the surface of planet where r

A stone is dropped by an astronaut from a height of 1.47 m above the surface of a planet. When stone reaches a point P at a height of 0.32 m it attains a speed of 4.1 m//s Is the planet earth ?

An object is dropped from an altitude of one Earth radius above Earth’s surface. If M is the mass of Earth and R is its radius. The speed of the object just before it hits Earth is given by: