Earth and moon centre distance is 'r'. From the mid point what should be the speed of the particle so that it can escape to infinity?

The radii of a planet and its satellite are 2r and r and their densities are rho and 2rho respectively. Their centres are separated by a distance d. The minimum speed with which a body should be projected from the mid point of the line joining their centres so that the body escapes to infinity is (G-universal gravitational constant)

a narrow tunnel is dug along the diameter of the earth, and a particle of mass m_(0) is placed at R/2 distance from the centre. Find the escape speed of the particle from that place.

A very small groove is made in the earth, and a particle of mass m_(0) is placed at (R)/(2) distance from the centre. Find the escape speed of the particle fro that place.

The value of escape speed from the surface of earth is

What is the average distance of moon from earth ?

The escape speed of a body from the surface of the Earth is

If d is the distance between the centre of the earth of mass M_(1) and the moon of mass M_(2) , then the velocity with which a body should be projected from the mid point of the line joining the earth and the moon, so that it just escape is

A body at rest starts from a point at a distance r (gtR) from the centre of the Earth. If M and R stand for the speed of the body when it reaches the Earth surface is

A particle is projected from the mid-point of the line joining two fixed particles each of mass m . If the separation between the fixed particles is l , the minimum velocity of projection of the particle so as to escape is equal to

A tunnel is dug along a chord of the earth at a perpendicular distance R//2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall, and the acceleration of the particle vary with x (distance of the particle from the centre) according to