Two planets move around the sun. The periodic times and the mean radii of the orbits are ${T_1},\,{T_2}$ and ${r_1},\,{r_2}$ respectively. The ratio ${T_1}/{T_2}$ is equal to
${({r_1}/{r_2})^{1/2}}$
${r_1}/{r_2}$
${({r_1}/{r_2})^2}$
${({r_1}/{r_2})^{3/2}}$
A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )
When a body is taken from pole to the equator its weight
Time period of simple pendulum increases by an amount $\sqrt 2 $ times at height $'h'$ from the surface of earth. Then the value of $h$ is
The value of escape velocity on a certain planet is $2\, km/s$ . Then the value of orbital speed for a satellite orbiting close to its surface 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 $(V)$ ?