The maximum height of a mountain on earth is limited by the rock flowing under the enormous weight above it. Studies show that maximum height depends on young’s modulus (Y) of the rod, acceleration due to gravity (g) and the density of the rock (d).
(a) Write an equation showing the dependence of maximum height (h) of mountain on Y, g and d. It is given that unit of Y is `Nm^(-2)`.
(b) Take `d = 3 xx 10^(3) kg m^(-3), Y = 1 xx 10^(10) Nm^(-2) and g = 10 ms^(-2)` and assume that maximum height of a mountain on the surface of earth is limited to 10 km [height of mount Everest is nearly 8 km]. Write the formula for h.