A liquid of volumetric thermal expansion coefficient = `gamma` and bulk modulus B is filled in a spherical tank of negligible heat expansion coefficient its radius R and wall thickness is t `(tleleR)` when the temperature of the liquid is raised by theta the tensile stress developed in the walls of th tank is:

Options

A. `BgammathetaR//2t`
B. `BgammathetaR//t`
C. `2BgammathetaR//t`
D. `BgammathetaR//4t`

Answer

A

Explanation

`DeltaV=VthetaY,DeltaV/V=Ytheta`
stress`=((DeltaV)/V)B`
`DeltaP=YthetaB`
`F/(piR^(2))=YthetaB`
`F=YthetaB(piR^(2))`
tensile stress`=F/(2piRt)=(YthetaB)/(2piRt)`
tensil stree `=((YthetaBR)/(2t))`