A solid block of silver with density `10.5 xx 10^(3) kg m^(-3)` is subjected to an external pressure of `10^(7) Nm^(-2)`. If the bulk modulus of silver is `17 xx 10^(10) Nm^(-2)`. Then the change in density of silver (in `kg m^(-3)`) is

Options

A. 0.61
B. 1.7
C. 6.1
D. `17 xx 10^(3)`

Answer

a

Explanation

`:'` change in volume, `Delta V = (Delta P.V)/(B)`
`V_(1) = V, V_(2) = V - Delta V`
`= V - (Delta P.V)/(B) implies (V)/(B) (B - Delta rho)`
`:'` mass of block does no change ltbgt `:. Rho_(1) v_(1) = rho_(2) V_(2) = M`
`implies rho_(1) V = rho_(2). (V)/(B) (B - Delta P)`
`implies rho_(2) = (rho_(1) B)/((B - Delta P))`
`:.` Change in density of silver block
`Delta rho = rho_(2) - P_(1)`
`=( rho_(B))/(B - Delta P) - rho_(1) implies (rho_(1) Delta P)/(B - Delta P)`
`Delta rho = (rho_(1) Delta P)/(B- Delta P) = (10.5 xx 10^(3) xx 10^(7))/(17 xx 10^(10) - 10^(7))`
`= (10.5 xx 10^(10))/(1.6999 xx 10^(11)) = 6.176 xx 10^(-1)`
`0.6176 kgm^(-3)`