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For a constant hydraulic pressure on an ...

For a constant hydraulic pressure on an object, the fractional change in the object's volume `((Delta V)/(V))` and its compressibility `((1)/(K))` are related as

A

`(Delta V)/(V) prop K`

B

`(Delta V)/(V) prop K^(2)`

C

`(Delta V)/(V) prop (1)/(K)`

D

`(Delta V)/(V) prop (1)/(K^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Bulk modulus `K = (V dP)/(dV)` (numercially)
`:. (1)/(K) = (dV)/(V(dP))`
`:. (dV)/(V) = (dP)/(K)` if dP is kept constant
Then `(dV)/(V) prop (1)/(K)`
where `((1)/(K))` is the compressibility of the object.
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