Assuming Earth to be a sphere of uniform density,what is the value of gravitational acceleration in a mine $100 \, km$ below the Earth's surface? (Given $R = 6400 \, km$,$g = 9.8 \, m/s^2$)

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is

During the motion of a man from the equator to the pole of the Earth,his weight will ....... $\%$ (neglect the effect of change in the radius of the Earth).

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on $60^o$ latitude becomes zero is (Radius of earth $= 6400 \, km$. At the poles $g = 10 \, m/s^2$)

When a ball is dropped from a height $h$,it takes $t \ s$ to reach the ground. If the same experiment is done on a different planet having a mass $100$ times the earth's mass and a radius $10$ times the earth's radius,then the time it will take to cover the same height on the new planet is:

The mass of the moon is $7.34 \times 10^{22} \ kg$ and the radius of the moon is $1.74 \times 10^6 \ m$. The value of gravitational acceleration on the moon will be ....... $N/kg$.