The gravitational potential energy of a system of three masses $m$,$2m$,and $3m$ placed at the three vertices of an equilateral triangle of side '$a$' is:

The particles $A$ and $B$ of mass $m$ each are separated by a distance $r$. Another particle $C$ of mass $M$ is placed at the midpoint of $A$ and $B$. Find the work done in moving $C$ to a point equidistant $r$ from $A$ and $B$ without acceleration. ($G$ is the gravitational constant and only gravitational interaction between $A, B$ and $C$ is considered.)

Which of the following most closely depicts the correct variation of the gravitational potential $V(r)$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)

In a gravitational field,at a point where the gravitational potential is zero,

What is the potential energy of a satellite at a height of $6.4 \times 10^6 \, m$ from the surface of the Earth? ($R_e$ = radius of the Earth)

$A$ thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the center of the circle?