The mass of the earth is $81$ times that of the moon and the radius of the earth is $3.5$ times that of the moon. The ratio of the acceleration due to gravity at the surface of the moon to that at the surface of the earth is

The mass of a planet is $\frac{1}{10}^{\text {th }}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

The mass of the moon is $\frac{1}{{81}}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

If the radius of the earth be increased by a factor of $5,$ by what factor its density be changed to keep the value of $g$ the same ?

Let $\omega$ be the angular velocity of the earth’s rotation about its axis. Assume that the acceleration due to gravity on the earth’s surface has the same value at the equator and the poles. An object weighed at the equator gives the same reading as a reading taken at a depth d below earth’s surface at a pole $(d < < R)$ The value of $d$ is

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