Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $d=\frac{R}{2}$ from the surface of earth, if its werght on the surface of earth is $200\,N$, will be $………..\,N$ ( $Given R =$ Radrus of earth)

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 $h_Q$ ?

If the Earth has no rotational motion, the weight of a person on the equator is $W$. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $\frac{3}{4}\,W$ . Radius of the Earth is $6400\, km$ and $g = 10\, m/s^2$

A uniform spherical planet (Radius $R$) has acceleration due to gravity at its surface $g.$ Points $P$ and $Q$ located inside and outside the planet have acceleration due to gravity $\frac{g}{4} .$ Maximum possible separation between $P$ and $Q$ is

If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.