Acceleration due to gravity on moon is $\frac 16$ of the acceleration due to gravity on earth. If the ratio of densities of earth $({\rho _e})$ and moon $({\rho _m})$ is $\left( {\frac{{{\rho _e}}}{{{\rho _m}}}} \right) = \frac{5}{3}$ then radius of moon $R_m$ in terms of $R_e$ will be

Weight of a body is maximum at

A person will get more quantity of matter in $kg -wt$ at

Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{p}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R} / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{p}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{p}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_Q$ ?

A planet of radius $R =\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3} \ kgm ^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth $=6 \times 10^6 \ m$ and the acceleration due to gravity on Earth is $10 \ ms ^{-2}$ )