Imagine a planet with a non-uniform density distribution. Its core has a density $\rho_c$, and the outer shell has a density $\rho_s$. If the core radius is half the total radius R, what core density $\rho_c$ would result in the same surface gravity as Earth (assuming the shell density $\rho_s$ is negligible)?

An object experiences a gravitational force of $100$ N on the surface of the earth. What is the gravitational force on it at a height equal to one-third the radius of the earth?

Given below are two statements: One is labelled as

Assertion A and the other is labelled as Reason R.

Assertion A: A pendulum clock when taken to

Mount Everest becomes fast.

Reason R: The value of $g$ (acceleration due to

gravity) is less at Mount Everest than its value on the

surface of earth.

In the light of the above statements, choose the

most appropriate answer from the options given

below

If Earth's radius were doubled while its mass remained constant, the acceleration due to gravity at its surface would:

Which is constant for a satellite in orbit

Let $A$ and $B$ be the points respectively above and below the earth's surface each at a distance equal to half the radius of the earth. If the acceleration due to gravity at these points be $g_A$ and $g_B$ respectively, then $g_B: g_A$

When you move from equator to pole, the value of acceleration due to gravity ( $\mathrm{g}$ )

If the radius of the earth shrinks by $2.0 \%$, mass remaining constant, then how would the value of acceleration due to gravity change?

To what latitude does the SYNCOMS coverage extend? What is the orbital speed of a SYNCOMS?

If the earth were made of lead of relative density 11.3, what then would be the value of acceleration due to gravity on the surface of the earth? Radius of the earth $=6.4 imes 10^6 \mathrm{~m}$ and ${G}=6.67 imes 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$.

If the earth stops rotating about its axis, then the magnitude of gravity