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 bluk modulus of the metal, then find the ratio `rho'//rho`.

Options

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

Answer

B

Explanation

Bulk modulus `(B) = (Delta P)/(-Delta ""^(V)//_(V))`
`= (-Delta P)/((V_(2))/(V_(1))-1) rArr B= (P)/(1- (rho)/(rho'))rArr 1- (rho)/(rho') = (P)/(B)`
`1- (P)/(B)= (rho)/(rho)`
`(rho')/(rho) = (1)/(1- (P)/(B))`