Weight of a body is maximum at

The mass of a planet is $\frac{1}{9}$ of the mass of the Earth and its radius is half that of the Earth. If a body weighs $9 \ N$ on the Earth,its weight on the planet would be ........ $N$.

The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as at present weight is ($g=$ gravitational acceleration,$R=$ equatorial radius of the earth).

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9 : 4$. The mass of the planet is $\frac{1}{9}^{th}$ of that of the Earth. If $R$ is the radius of the Earth,what is the radius of the planet? (Assume the planets have the same mass density)

$A$ newly discovered planet has a density eight times the density of the earth and a radius twice the radius of the earth. The time taken by a $2\, kg$ mass to fall freely through a distance $S$ near the surface of the earth is $1$ second. Then the time taken for a $4\, kg$ mass to fall freely through the same distance $S$ near the surface of the new planet is ....... $\sec$.

The radius of the Earth is about $6400 \; km$ and that of Mars is $3200 \; km$. The mass of the Earth is about $10$ times the mass of Mars. An object weighs $200 \; N$ on the surface of the Earth. Its weight on the surface of Mars will be .......... $N$.