$A$ body of mass $m$ rises to a height $h = R/5$ from the earth's surface,where $R$ is the earth's radius. If $g$ is the acceleration due to gravity at the earth's surface,the increase in potential energy is:

The gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the Earth is $U$. Express the weight of the body at this point in terms of $U$.

$A$ stationary body on the surface of the Earth has negative potential energy. What does this indicate?

$A$ star is modeled as a uniform spherical distribution of matter,keeping the mass of the star constant. How does the gravitational pressure on the surface depend on the volume of the star?

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Can never be positive.	$(a)$ Escape velocity
$(2)$ Reason for negative potential energy of galaxies.	$(b)$ Gravitational potential energy
	$(c)$ The nature of force between different galaxies is attractive.

An infinite number of objects,each of mass $1 \ kg$,are placed on the $x$-axis on both sides of $x=0$ at positions $x = \pm 1 \ m, \pm 2 \ m, \pm 4 \ m, \pm 8 \ m, \ldots$ and so on. The magnitude of the resultant gravitational potential (in $SI$ units) at $x=0$ is ($G$ is the universal gravitational constant).