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

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 ? (Take the planets to have the same mass density)

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

A man of $50\, kg$ mass is standing in a gravity free space at a height of $10\, m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed $2\, m/s$. When the stone reaches the floor, the distance of the man above the floor will be ...... $m$

${g_e}$ and ${g_p}$ denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice as that of earth. Then

For a satellite to orbit around the earth, which of the following must be true ?