Calculate energy needed for moving a mass of $4\,\,kg$ from the centre of the earth to its surface (in joule), if radius of the earth is $6400\,\, km$ and acceleration due to gravity at the surface of the earth is $g = 10 \,\,m/sec^2.$

A particle starts from rest at a distance $R$ from the centre and along the axis of a fixed ring of radius $R \&$ mass $M.$ Its velocity at the centre of the ring is :

A small ball of mass $‘m’$ is released at a height $‘R’$ above the earth surface, as shown in the figure above. If the maximum depth of the ball to which it goes is $R/2$ inside the earth through a narrow grove before coming to rest momentarily. The grove, contain an ideal spring of spring constant $K$ and natural length $R,$ find the value of $K$ if $R$ is radius of earth and $M$ mass of earth

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy ${E_0}$. Its potential energy is

A satellite with kinetic energy ${E_k}$ is revolving round the earth in a circular orbit. How much more kinetic energy should be given to it so that it may just escape into outer space