$A$ man can jump to a height of $1.5 \, m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are,respectively,one-quarter and one-third that of planet $A$?

The magnitudes of the gravitational field at distances $r_1$ and $r_2$ from the center of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then:

If the mass of Earth is $80$ times that of a planet and its diameter is double that of the planet,and $g$ on Earth is $9.8 \ m/s^2$,then the value of $g$ on that planet is ........ $m/s^2$.

$A$ body has a weight of $90 \ kgf$ on the earth's surface. The mass of the moon is $1/9$ of the earth's mass and its radius is $1/2$ of the earth's radius. On the moon,the weight of the body is .......... $kgf$.

Two particles are projected vertically upwards with the same velocity on two different planets with accelerations due to gravity $g_1$ and $g_2$ respectively. If they fall back to their initial points of projection after lapse of times $t_1$ and $t_2$ respectively,then

The diameters of two planets are in the ratio $4:1$. Their mean densities have the ratio $1:2$. The ratio of gravitational acceleration on the surface of the planets will be: