The density of a metal at normal pressure is `rho`, Its density when it is subjected to an excess pressure `rho` is `rho'` IF B is bulk modulus of the metal, the ratio of `(rho')/rho` is
A
`1+B/p`
B
`1/(1-p/B)`
C
`1+p/B`
D
`1/(1+p/B)`
Text Solution
Verified by Experts
The correct Answer is:
B
Volume strain= change in pressure=p Initial volume `V=M/P` Final volume , `V.=M/(rho.)` Change in volume , `V.=V=M((rho-rho.)/(rho.rho))` `therefore` Volume strain = `(V.-V)/V=(rho-rho.)/(rho.)` `therefore B=(pV)/(V.-V)=(ptimesrho.)/(rho-rho.)` or,`p/B=(rho-rho.)/(rho.)=(rho.-rho)/(rho.)` or, `rho/(rho.)=1-p/B` `therefore(rho.)/rho=1/(1-p/B)`
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