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. Simple answer in equations
The value of the gravitational field strength is determined by the mass of an object and the distance from the center of that object.
At the base of the mountain, the distance from the center of the planet to the base of the mountain is R + 2000 m (where R is the radius of the planet).
At the top of the mountain, the distance from the center of the planet to the top of the mountain is R + (2000 + 2000) m (taking into account the extra height of the mountain).
Since the difference in height between the two locations is relatively small compared to the radius of the planet, the change in distance is negligible. Therefore, the value of the gravitational field strength at the base of the mountain and at the top of the mountain are almost equal.
Mathematically, we can represent this as:
g_base ≈ g_top
Where g_base is the gravitational field strength at the base of the mountain and g_top is the gravitational field strength at the top of the mountain.