Figure shows variation of acceleration due to gravity with distance from centre of a  uniform spherical planet, Radius of planet is $R$. What is $r_2 -r_1.$

A hemisspherical shell of mass $2M$ and radius $6R$ and a point mass $M$ are performing circular motion due to their mutual gravitational interaetion Their positions are shown in figure at any moment of time during motion. If $r_1$ and $r_2$ are the radii of circular path of hemispherical shell and point mass respectively and ${\omega _1}$ and  ${\omega _2}$ are the angular speeds of hemi-spherical shell and point mass respectively, then choose the correct option

Acceleration due to gravity at surface of a planet is equal to that at surface of earth and density is $1.5$ times that of earth. If radius of earth is $R$, radius of planet is .................

A mass falls from a helght $h$ and its time of fall $t$ is recorded in terms of time period $T$ of a simple pendulum. On the surface of earth it is found that $t =2 T$. The entre setup is taken on the surface of another planet whose mass is half of that of earth and radius the same. Same experiment is repeated and corresponding times noted as $t'$ and $T'$.

The height at which the weight of a body  becomes ${\frac{1}{16}}^{th}$ , its weight on the surface of earth (radius $R$), is

Mass of moon is $7.34 \times {10^{22}}\,kg$. If the acceleration due to gravity on the moon is $1.4\,m/{s^2}$, the radius of the moon is $(G = 6.667 \times {10^{ - 11}}\,N{m^2}/k{g^2})$