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A liquid of volumetric thermal expansion coefficient $γ$ and the bulk modules B is filled in a spherical tank of negligible heat expansion coefficient. Its radius is R and wall thickness is 't' $(t < < R)$ . when the temperature of the liquid is raised by $θ$ , then the tensile stress developed in the walls of the tank is:

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B γ θ R / 2 t

B γ θ R / t

2 B γ θ R / t

B γ θ R / 4 t

answer is A.

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Detailed Solution

$Δ V = VθY \Rightarrow \frac{Δ V}{V} = yθ$

$Stress = (\frac{Δ V}{V}) B \Rightarrow Δ P = γθB$

$\frac{F}{{πR}^{2}} = γθB \Rightarrow F = {πγθBR}^{2}$
Tensile stress $= \frac{F}{2 πRt} = \frac{{πγθBR}^{2}}{2 πRt} = (\frac{γθBR}{2 t})$

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