Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre ofthe planet for $r \ge $ radius of the planet. Plots $1$ and $2$ coincide for $r \ge {R_2}$ and plots $3$ and $4$ coincide for $r \ge {R_4}$ . The sequence of the planets in the descending order of their densities is
$1, 2, 3, 4$
$4, 3, 2, 1$
$2, 1, 4, 3$
$1, 2, 4, 3$
If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
If the radius of the earth were shrink by $1\%$ and its mass remaining the same, the acceleration due to gravity on the earth's surface would
A satellite of mass $m$ is at a distance $a$ from $a$ star of mass $M$. The speed of satellite is $u$. Suppose the law of universal gravity is $F = - G\frac{{Mm}}{{{r^{2.1}}}}$ instead of $F = - G\frac{{Mm}}{{{r^2}}}$, find the speed of the statellite when it is at $a$ distance $b$ from the star.
The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)
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