The radius of the Earth is approximately $6000 \, km$. The weight of a body at a height of $6000 \, km$ from the Earth's surface becomes:

Assume that a tunnel is dug through the Earth from the North Pole to the South Pole and that the Earth is a non-rotating,uniform sphere of density $\rho$. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the center of the Earth is:

$A$ body of mass $m$ is taken to the bottom of a deep mine. Then

As we go from the equator of the earth to the pole of the earth,the value of acceleration due to gravity

What should be the angular speed of the Earth about its axis so that the acceleration due to gravity at the equator becomes zero?

The acceleration due to gravity on the moon is $\frac{1}{6}$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_e$ to the density of the moon $\rho_m$ is $\frac{5}{3}$,then the radius of the moon $R_m$ in terms of the radius of the earth $R_e$ is: