The density of a metal at normal pressure is `rho`. Its density when it is subjected to an excess pressure p is `rho'` . If B is the bulk moldulus of the metal, the ratio `(rho')/(rho)` is

Options

A. `1+p//B`
B. `1+B//p`
C. `(1)/((1-B//p))`
D. `(1)/((1-p//B))`

Answer

D

Explanation

(d) Bulk modulus `B=(p)/(dV//V)` or `dV=(pV)/(B)`
`therefore " "rho'=(M)/(V-dV)=(M)/(V-(pV//B))`
`=(M)/(V(1-p//B))=(rho)/((1-p//B))`
`therefore (rho')/(rho)=(1)/((1-p//B))`