The ratio of the accelerations due to gravity at heights $1280 \ km$ and $3200 \ km$ above the surface of the earth is (Radius of the earth $= 6400 \ km$)

Two planets have radii $r_1$ and $r_2$ and their densities are $p_1$ and $p_2$ respectively. The ratio of the acceleration due to gravity on their surfaces will be:

The average density of the Earth is [ $g$ is acceleration due to gravity]:

When a body is taken from the equator to the poles,its weight

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 ......... $m/s^2$.

What should be the angular speed of the Earth so that a body at $60^{\circ}$ latitude becomes weightless? (Radius of Earth $R = 6400 \, km$)