The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain `((DeltaV)/(V))^(2)`

Options

A. `B^(2)((DeltaV)/(V))`
B. `B((DeltaV)/(V))^(2)`
C. `(1)/(B)((DeltaV)/(V))`
D. `B((DeltaV)/(V))`

Answer

D

Explanation

(d) `B=("Normal stress")/("Volume strain")=|(p)/(-((DeltaV)/(V)))|=|-(pV)/(V)|`
`p=V(DeltaV)/(V)=B((DeltaV)/(V))`
where, normal stress =p, volume strain `=-(DeltaV)/(V)`