question_answer 7)

A vertical off-shore structure is built to withstand a maximum stress of \[{{10}^{9}}\,Pa\]. Is the structure suitable for putting upon top of an oil well in Bombay High? Take the depth of the sea to be roughly 3 km, and ignore ocean currents.

Answer:

Here, maximum stress \[={{10}^{9}}\,Pa,\,\,h=3\,km=3\times {{10}^{3}}\,m;\] \[p(\text{water})={{10}^{3}}\,kg/{{m}^{3}}\] and \[{{h}_{1}},{{h}_{2}}\]. The structure will be suitable for putting upon top of an oil well provided the pressure exerted by sea water is less than the maximum stress it can bear. Pressure due to sea water, \[{{\text{h}}_{\text{1}}}\text{=}\frac{\text{2Scos }\!\!\theta\!\!\text{ }}{{{\text{r}}_{\text{1}}}\text{ }\!\!\rho\!\!\text{ g}}\] Since the pressure of sea water is less than the maximum stress of 109 Pa, the structure will be suitable for putting upon top of the oil well.