$A$ spherical planet far out in space has a mass $M_0$ and diameter $D_0$. $A$ particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

The weights of an object are measured in a coal mine of depth $h_1$,then at sea level of height $h_2=0$,and lastly at the top of a mountain of height $h_3$ as $W_1, W_2$,and $W_3$ respectively. Which one of the following relations is correct? [$h_1 \ll R, h_3 \ll R, R=$ radius of the earth]

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 acceleration due to gravity on the planet $A$ is $9$ times the acceleration due to gravity on planet $B$. $A$ man jumps to a height of $2 \,m$ on the surface of $A$. What is the height of jump by the same person on the planet $B$?

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:

How does the acceleration due to gravity $(g)$ at a location on Earth change with latitude?