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Q.

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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a

2BγθR/t  

b

BγθR/t  

c

BγθR/4t    

d

BγθR/2t  

answer is A.

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Detailed Solution

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 ΔV=VθY⇒ΔVV=yθ

 Stress =ΔVVB⇒ΔP=γθB

FπR2=γθB⇒F=πγθBR2 
Tensile stress =F2πRt=πγθBR22πRt=γθBR2t   

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