Question

If a solid will break under pressure greater than `13atm` and that solid has specific gravity of 4, what is maximum height of a circular column made from the solid that can be built at the earth's surface?( Note: `1atm = 10^5 Pa`), `g = 10m/s^2`

Answer 1

Let us consider unit area of the column of solid of safe height `h`.

Pressure `P_T` created at the lowest part of the column is sum of pressure due to the weight of the column and atmospheric pressure `P_A`. The pressure equation becomes

`P_A + h rhog = P_T`
where `rho` is the density of solid and `g` is acceleration due gravity.
`=>h = (P_T-P_A)/(rhog)`

Inserting given values we get

`h = (13xx10^5-10^5)/((4xx10^3)xx10)`
`=>h = (12xx10^5)/(4xx10^4)`
`=>h=30\ m`