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)

The centre of gravity of a body on the earth coincides with its centre of mass for a small object,whereas for an extended object,it may not. What is the qualitative meaning of 'small' and 'extended' in this regard? For which of the following does the centre of gravity coincide with the centre of mass: a building,a pond,a lake,a mountain?

$A$ body weighs $72 \ N$ on the surface of the earth. What is the gravitational force on it at a height equal to half the radius of the earth (in $N$)?

If the density of the Earth increases $4$ times and its radius becomes half of its present value,our weight will

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is