The gravitational field due to a mass distribution is $E = K/x^3$ in the $X$-direction ($K$ is a constant). Taking the gravitational potential to be zero at infinity,its value at a distance $x$ is:

Define gravitational potential. Give its unit. Is gravitational potential a vector or a scalar quantity?

$A$ point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre $C$. When released,it reaches $C$ under the gravitational attraction of the ring. Its speed at $C$ will be

$A$ geostationary satellite orbits the Earth at a height of nearly $36,000 \; km$ from the surface of the Earth. What is the potential due to Earth's gravity at the site of this satellite? (Take the potential energy at infinity to be zero). Mass of the Earth $= 6.0 \times 10^{24} \; kg$,radius $= 6400 \; km$.

$A$ body of mass $m$ is kept at a small height $h$ above the ground. If the radius of the earth is $R$ and its mass is $M$,the potential energy of the body and earth system (with $h = \infty$ being the reference position) is

$A$ body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth $(R_e)$. The increase in potential energy will be . . . . . . . ($g$ is acceleration due to gravity at the surface of earth)