The time period of a simple pendulum on a freely moving artificial satellite is

The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A: g_B\right)$ will be

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be........ $m/{s^2}$ . $(g = 9.8\,m/{s^2})$

A certain planet completes one rotation about its axis in time $T$. The weight of an object placed at the equator on the planet's surface is a fraction $f(f$ is close to unity) of its weight recorded at a latitude of $60^{\circ}$. The density of the planet (assumed to be a uniform perfect sphere) is given by

Two equal masses $m$ and $m$ are hung from a balance whose scale pans differ in vertical height by $'h'$. The error in weighing in terms of density of the earth $\rho $ is

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