If both the mass and the radius of the earth decrease by $1\%$, the value of the acceleration due to gravity will

The acceleration due to gravity near the surface of a planet of radius $R$ and density $d$ is proportional to

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

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

During motion of a man from equator to pole of earth, its weight will ....... $\%$ (neglect the effect of change in the radius of earth)

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