A certain planet is a uniform sphere of mass M and radius R of 5.1 x 10^6 m. A Mountain on the surface of the planet has a height of 2000 m. Suggest why the value of the gravitational field strength at the base of the mountain and at the top of the mountain are almost equal.
The value of the gravitational field strength is determined by the distribution of mass within a planet.
Since the planet is a uniform sphere, the mass is distributed symmetrically around its center. As a result, the gravitational pull experienced at any point on the surface of the planet is due to the mass located below that point.
When we consider the gravitational field strength at the base of the mountain, the mass of the mountain itself does not contribute significantly to the gravitational attraction because it is located above the base. The dominant contribution comes from the mass located below the base, which is essentially the same regardless of whether there is a mountain or not.
At the top of the mountain, although there is less mass located below, the gravitational force due to the mountain itself also becomes significant. However, since the height of the mountain (2000 m) is relatively small compared to the radius of the planet (5.1 x 10^6 m), the additional mass of the mountain does not significantly alter the gravitational field strength.
Therefore, due to the symmetric distribution of mass in the planet and the relatively small height of the mountain compared to the radius of the planet, the gravitational field strength at the base and top of the mountain are almost equal.