Assume that mountains higher than 10 km do not exist on Earthbecause bigger mountains could not be supported by the strength ofrock at their bases. The pressure at the middle of the base of amountain is equal to the weight of a column of rock (with unitcross section area) as high as the mountain. The pressure at thebase of taller mountains would exceed the strength of the rock andthe mountain would slump.
For rock of identical density (3000 kg m-3 ) and crushingstrength, determine the maximum size cubic asteroid that could youcould make out of two identical blocks with dimensions of L, L andL/2. The two blocks put together make a cube.
For a larger sized asteroid, the pressure between cubes causedby gravitational attraction would exceed the rock’s yield strengthand it would flow - forming a more spherical shape. For calculationyou can assume that the mass of block is concentrated at its centerso that the pressure between the two blocks is just the forcebetween the centers of mass divided by the contact area.
