A material has normal density `rho` and bulk modulus `K`. The increase in the density of the material when it is subjected to an external pressure `P` from all sides is

Options

A. `(P)/(rhoK)`
B. `(K)/(rhoP)`
C. `(rhoP)/(K)`
D. `(rhoK)/(P)`

Answer

C

Explanation

`(rho^(`))/(rho)=`((M)/(V-triangleV))/((M)/(V))=(V)/(V-triangleV)`
or `(rho^(`))/(rho)=V(V-DeltaV)^(-1)`
or `(rho^(`))/(rho)=1+(triangleV)/(V)`
(Using Binomial Theoram)
or `(triangleV)/(V)=(rho^(`))/(rho)-1` or `(triangleV)/(V)=(rho^(`)-rho)/(rho)`
`K=(triangleP)/((triangleV)/(V))=(rho triangleP)/(rho^(`)-rho)` or `rho^(`)-rho=(rho triangleR)/(K)`
but `triangleP=P` (given)
`thereforerho^(`)-rho=(rhoP)/(K)`