The density of a solid at normal pressure is p. When the solid is subjected to an excess pressure `P_(1)`, the density changes top'. If the bulk modulus of the solid is k, then the ratio `(p')/p` is

Options

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

Answer

A

Explanation

Since density `p=m/V`
`thereforedp=(-m)/(V^(2))dV`
`therefore(dp)/P=(-dV)/V`
Substituting this value in bulk modulus, K`=(-P)/(dV//V)`
`K=(-P)/((-dp)/p)=(Pp)/(dp)`
with increase in pressure, the density increases
`thereforedp=p.-p`
`thereforeK=(Pp)/(p.-p)`
`therefore(p.-p)/p=p/K`
`(p.)/p=(1+p)/K`
so correct choice is (a).