The angular speed of the Earth,such that an object on the equator may appear weightless,is ($g = 10\,m/s^2$,radius of the Earth $R = 6400\,km$).

The value of $g$ at a particular point is $9.8\,m/s^2$. Suppose the Earth suddenly shrinks uniformly to half its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the Earth does not shrink) will now be ......... $m/s^2$.

Earth is assumed to be a sphere of radius $R$. If $g_{\phi}$ is the value of effective acceleration due to gravity at latitude $30^{\circ}$ and $g$ is the value at the equator,then the value of $|g - g_{\phi}|$ is ($\omega$ is the angular velocity of rotation of the Earth,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$).

At what distance above and below the surface of the earth will a body have the same weight? (Take the radius of the earth as $R$.)

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

Two planets have radii $R_1$ and $R_2$ and densities $\rho_1$ and $\rho_2$ respectively. Find the ratio of the acceleration due to gravity on these planets.