A ball is launched from the top of Mt. Everest which is at elevation of $9000 \,m$. The ball moves in circular orbit around earth. Acceleration due to gravity near the earth's surface is $g$. The magnitude of the ball's acceleration while in orbit is

There is no atmosphere on the moon because

The mass of a planet is $\frac{1}{10}^{\text {th }}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth is same as that of the acceleration due to gravity at a depth a depth $\alpha$ h $\left(h \ll R_{e}\right)$ from the earth surface. The value of $\alpha$ will be$….$(use $R _{ e }=6400\,km$ )

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine $100\, km$ below the earth’s surface …….. $m/{s^2}$. (Given $R = 6400 \,km$)