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 earth does not shrink) will now be ……… $m/{\sec ^2}$.

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is $……….km$ : [Radius of earth $R =6400 \,km$ and $\sqrt{3}=1.732]$

Weight of a body decreases by $1.5 \%$, when it is raised to a height $h$ above the surface of earth. When the same body is taken to same depth $h$ in a mine, its weight will show ……..

If earth is supposed to be a sphere of radius R, if $g_{30}$ is value of acceleration due to gravity at latitude of $ 30^\circ$ and g at the equator, the value of $g – {g_{{{30}^o}}}$ is

Two satellites $\mathrm{P}$ and $\mathrm{Q}$ are moving in different circular orbits around the Earth (radius $R$ ). The heights of $\mathrm{P}$ and $\mathrm{Q}$ from the Earth surface are $h_{\mathrm{p}}$ and $h_{\mathrm{Q}}$, respectively, where $h_{\mathrm{p}}=\mathrm{R} / 3$. The accelerations of $\mathrm{P}$ and $\mathrm{Q}$ due to Earth's gravity are $g_{\mathrm{p}}$ and $g_{\mathrm{Q}}$, respectively. If $g_{\mathrm{p}} / g_{\mathrm{Q}}=36 / 25$, what is the value of $h_Q$ ?