Himalaya to be eroded down ?

[ritva_1950]

12. Given that 1) the average density of the rock which comprises theHimalaya is 2.8 g/cm³, 2) the average density of lithospheric mantleis 3.3 g/cm³, 3) the maximum elevation of the Himalaya is 8.8 km,and 4) the average rate at which mountains are eroded is 0.2 mm/yr, calculatehow long it would take for the Himalaya to be eroded down to sea level. Showyour working.

Clue: You are provided with density data for a reason. Is it only 8.8 kmwhich needs to be eroded? What does Archimedes principle tell us?


hwo should I do?

 

[HallsofIvy]

Normally, if you were given that "the average rate at which mountains are eroded is .2 mm per year" and "the mountain is 8.8 km", we would say that 8.8km= 8800 m= 8800000 mm so at .2 mm per year it would take \(\displaystyle \frac{8800000}{.2}= 44000000\) years.

But here we are given that "The average density of the rock that comprise the Himalaya Mountains is 2.8 g/c^3" and "the average density of lithospheric mantle is 3.3 g/cm^3" and specifically told that "You are provided with density data for a reason". I suspect that the point is that the ".2 mm per year" applies to the "average" lithospheric mantle while the Himalaya Mountains are less dense, "softer", than that. What you have given here does not say how to correct for that but the simplest thing to do is assume the time required to erode will be proportional to density. The Himalayas are \(\displaystyle \frac{2.8}{3.3}\) as "hard" as average mountains so will erode in \(\displaystyle \frac{2.8}{3.3}(44000000)\) years.