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Is there some kind of math rule for how much does a mountain extends (depth) below the surface? Definitely! It is called isostasy. When I was a student, the lecture about isostasy started with a slide asking "why don't the mountains fall over?" (it may sound better in my native language..) First, some background: Mountains, and in general the Earth's ...


17

Forming of coastline During the last ice age, the North Sea was dry. When the ice melted sea levels slowly started to rise again and due to tides and currents a barrier of dunes was formed along what approximately is today's coast line. This created an area of land that fell dry during ebb-tide and flooded during high tide (this can still be seen in the '...


17

According to one survey using GPS mounted on a plateau below the summit, Mount Everest is increasing its height approximately 4mm each year. As for plate techtonics, this site describes it pretty simply: Much like a car crashing head-on with a truck, crumpling occurred when the two continents met and the result was the creation of the Himalayan Mountains....


15

Found an article that used a simple analytical modelling to determine how high a mountain can be. Reference Based on simple physics, tallest a mountain will be on Earth is ~10 km. This is based on: Simple cone shape for the mountain. Vol ≈ $r^2 h$ Based on weight of the mountain: Weight W ≈ $\rho g r^2 h$ Stress σ the mountain exerts on the ground ...


14

Factors determining the maximum possible height of mountains include the rate of uplift versus the rate of erosion[a] and rock strength. Rock strength is controlled by the type and internal structure of the rock in question. There is some evidence that once mountains extend above the snow line, glacial and periglacial erosion have a stronger control than ...


12

The glacial buzzsaw hypothesis (summary; sample paper) is that mountains can't get much higher than the elevation at which glaciers form cirques. The upper walls of the cirques are steep and erode easily, which planes off the peaks above them, shortening the mountains. The evidence is, to summarize, that they don't get much higher than the cirques. Cirques ...


9

Be warned this is a general (and speculative) answer, but it was getting too long to be a comment: The bulk of Greenland's ice mass is centred over inland/central Greenland. If you were to take all the ice away today, much of central Greenland would actually be below sea level, by several hundred metres in fact: Glacial isostatic rebound would seek to ...


7

To put it very short and sweet, yes, it is getting taller. It is getting taller because the Indian-Australian and the Eurasian plates are continuing to collide. Also, from what I have read, the amount by which its height increases every year is apparently somewhat undecided as some sources say it is growing by as much as 30" per year, while others say just ...


6

Altitudes are referred to a geoid (an imaginary surface of equal gravity strength), that is chosen to fit the mean sea level. Therefore, if we were to constantly adjust the geoid to fit the rising sea level, all the altitudes would indeed be decreasing in average. However, it is very important to highlight that "in average" part, because of the rates ...


5

Because it is not the strong portion that gets displaced. The mantle just below the crust bends, just like the crust above it, together they make up the lithosphere, It is not the thing being displaced it is the thing doing the displacing. The asthenosphere is being displaced. Your image is missing something important. Images courtesy of http://www....


5

The question seems to assume that the increase or decrease in mountain elevation is consistent and uniform, which it isn't. The Indian and Tibetan tectonic plates are converging in a NNE-SSW direction at an overall mean rate of between 26 and 36 mm per year. However, most of the time this convergence is taken up as static strain energy, released as elastic ...


4

I am assuming you are asking for the case of sea level being 200m higher and in isostatic equilibrium. In that case we can make use of Airy's isostasy model: https://en.wikipedia.org/wiki/Isostasy#Airy Applied to a water column over the mantle, you have to replace $\rho_c$ with your $\rho_w$. The total increase in ocean depth is $x = b_1 + h_1$, where $h_1$ ...


4

Continents move slowly. Glaciations are ephemeral in comparison. That said, there apparently is a huge connection between plate tectonics and whether the Earth is in icehouse or hothouse conditions. There was very little if any ice on the Earth when the Earth was in hothouse (aka greenhouse) conditions. Dinosaurs roamed close to the poles. The Earth's ...


3

Your approach of adding all the forces together is correct. You have a mistake in in the solution of the $F_{oc}$ integral, though. You forgot to integrate the terms $\rho_{w}gh_{w}$ and $-\rho_{oc}gh_{w}$ It should read: $F_{oc} = ... = \rho_{w}gh_{w}(h_{w}+h_{oc}) - \rho_{w}gh_{w}h_{w} + 0.5\rho_{oc}g(h_{w}+h_{oc})^{2} - 0.5\rho_{oc}gh_{w}^{2} - \rho_{oc}...


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