Physics · Mechanical Properties Of Solids · NEET
It is a shear problem, not pressure. Pressure (bulk stress) acts equally from all sides. But a mountain's base is squeezed from the top while its sides are free (open to air). This uneven loading creates a shear component roughly equal to h*rho*g. When this shear stress reaches the value at which rock flows, the base deforms and the mountain cannot rise further. So the limit uses the elastic limit / critical shear stress of rock, not the bulk modulus.
At the base, the stress from the weight above is stress = h*rho*g, where h is height, rho is the density of rock, and g is gravity. Set this equal to the elastic limit S of the rock: h*rho*g = S, so h = S / (rho*g). Using S = 30 x 10^7 N/m^2, rho = 3 x 10^3 kg/m^3, and g = 10 m/s^2 gives h = 10 km, which is taller than Mt. Everest (about 8.85 km).
Rock does not need to snap to stop the mountain from growing. Once the shear stress passes the elastic limit, the rock at the base starts to flow (deform permanently) instead of springing back. Flowing rock spreads out and stops the base from holding more height. So the correct condition is stress at base < elastic (critical shear) stress of rock.
Take a column of rock of height h and cross-section area A. Its volume is A*h, its mass is rho*A*h, and its weight is rho*A*h*g. Stress is force per area = weight / A = (rho*A*h*g)/A = h*rho*g. Notice A cancels, so the base stress depends only on height, density, and g, not on how wide the mountain is.
Yes. From h = S / (rho*g), a smaller g gives a larger maximum height. This is why mountains on Mars (lower g) can be far taller than Everest. On Earth, g is about 10 m/s^2, which is why the limit works out near 10 km.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
About 10 km, from h = S/(rho*g) using the elastic limit of rock. This is why no mountain, including Mt. Everest at about 8.85 km, exceeds roughly this value.
The elastic limit of rock in shear (critical shear stress at which rock flows). It is not the Young's modulus or bulk modulus; it is the stress the rock can take before it flows.
No. The base stress is h*rho*g, and the cross-section area cancels out. Only height, rock density, and g decide the limit.
Elastic limit S = 30 x 10^7 N/m^2, density rho = 3 x 10^3 kg/m^3, and g = 10 m/s^2, giving h = 10 km.
