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. using only equations
The gravitational field strength at a certain point depends on the mass and the distance from the center of the planet.
At the base of the mountain, the distance from the center of the planet is R (radius of the planet), and the mass of the planet is M.
At the top of the mountain, the distance from the center of the planet is slightly more than R (radius of the planet plus the height of the mountain). The mass of the planet is still M.
The equation for the gravitational field strength is given by:
g = (G * M) / (R^2)
Where g is the gravitational field strength, G is the gravitational constant, M is the mass of the planet, and R is the distance from the center of the planet.
Since the mass of the planet and the gravitational constant do not change, the only factor that affects the gravitational field strength is the distance from the center of the planet.
Because the height of the mountain (2000 m) is typically much smaller compared to the radius of the planet (5.1 x 10^6 m), the difference in distance between the top and the base of the mountain is negligible. Therefore, the gravitational field strength at the base and the top of the mountain are almost equal.