Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r\geq $ radius of the planet. Plots $1$ and $2$ coincide for $r\geq R_2$ and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is
$1$, $2$, $3$, $4$
$4$, $3$, $2$, $1$
$2$, $1$, $4$, $3$
$1$, $2$, $4$, $3$
The potential energy of a satellite of mass $m$ and revolving at a height $R_e$ above the surface of earth where $R_e =$ radius of earth, is
If the gravitational potential on the surface of earth is $V_0$, then potential at a point at height half of the radius of earth is ..........
Starting from the centre of the earth having radius $R,$ the variation of $g$ (acceleration due to gravity) is shown by
A planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct ?
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