$A$ uniform solid sphere of mass $M$ and radius $a$ is surrounded by a concentric uniform thin spherical shell of mass $0.5 M$ and radius $1.5 a$. The gravitational potential energy of a unit mass kept at a distance of $2.5 a$ from the center is

$A$ person brings a mass of $1 \ kg$ from infinity to a point $A.$ Initially,the mass was at rest but it moves at a speed of $3 \ m/s$ as it reaches $A.$ The work done by the person on the mass is $-5.5 \ J.$ The gravitational potential at $A$ is $:$ (in $J/kg$)

In some region,the gravitational field is zero. The gravitational potential in this region

Which curve depicts the variation of gravitational potential $V$ of a hollow sphere of radius $R$ with distance $r$ from its center?

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

If one wants to remove all the mass of the earth to infinity in order to break it up completely,the amount of energy that needs to be supplied will be $\frac{x}{5} \frac{GM^2}{R}$,where $x$ is .......... (Round off to the Nearest Integer). ($M$ is the mass of earth,$R$ is the radius of earth,$G$ is the gravitational constant)