With what velocity should a particle be projected so that its height becomes equal to the radius of the Earth?

$A$ body starts from rest from a distance $R_0$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ($R=$ radius of earth,$M=$ mass of earth).

$A$ body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is (where $g$ is acceleration due to gravity at the surface of the earth).

Two uniform solid spheres of equal radii $R$,but mass $M$ and $4M$ have a centre-to-centre separation $6R$,as shown in the figure. The two spheres are held fixed. $A$ projectile of mass $m$ is projected from the surface of the sphere of mass $M$ directly towards the centre of the second sphere. Obtain an expression for the minimum speed $v$ of the projectile so that it reaches the surface of the second sphere.

Under the influence of a central force,which of the following is conserved?

Two hypothetical planets of masses $m_1$ and $m_2$ are at rest when they are at an infinite distance apart. Because of the gravitational force,they move towards each other along the line joining their centres. What is their speed when their separation is $d$? (Speed of $m_1$ is $v_1$ and that of $m_2$ is $v_2$)