Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
${R^{\left( {\frac{{n + 1}}{2}} \right)}}$
${R^{\left( {\frac{{n - 1}}{2}} \right)}}$
${R^n}$
${R^{\left( {\frac{{n - 2}}{2}} \right)}}$
The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be
A body of mass $m$ is situated at a distance equal to $2R$ ($R-$ radius of earth) from earth's surface. The minimum energy required to be given to the body so that it may escape out of earth's gravitational field will be
Asatellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.02\,R.$ The period of second satellite is larger than the first one by approximately ........ $\%$
In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth, the work done is
In a certain region of space, the gravitational field is given by $-k/r$ , where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ be $V_0$ , then what is the expression for the gravitational potential $(V)$ ?