The highest temperature, density, and pressure on Earth are found:

At a height of $10 \,km$ above the surface of the earth,the value of acceleration due to gravity is the same as that at a particular depth below the surface of the earth. Assuming uniform mass density for the earth,the depth is ............. $km$.

Suppose a vertical tunnel is dug along the diameter of the Earth,which is assumed to be a sphere of uniform mass having density $\rho$. If a body of mass $m$ is dropped into this tunnel,its acceleration at a distance $y$ from the center is given by

Derive the equation for the variation of $g$ due to height from the surface of the Earth.

$A$ spherical planet has a mass $M$ and diameter $D$. $A$ particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity equal to:

$A$ hole is drilled through the Earth along a diameter and a stone is dropped into it. When the stone reaches the center of the Earth,which of the following quantities remains constant?