The density `rho` of water of buk modulus B at a depth y then ocean is related to the density at surface `rho_(0)` by the relation

Options

A. `rho = rho _(0) [1- ( rho _(0) g y )/(B) ]`
B. `rho = rho _(0) [ 1+ (rho _(0) g y )/( B)]`
C. `rho = rho _(0) [1 + (B)/( rho _(0) hgy)]`
D. `rho = rho_(0) [1- (B)/( rho _(0) gy)]`

Answer

B

Explanation

Bulk modulus, `B =- v _(0) (Delta p )/( Delta v) implies Delta V =- v _(0) ( Delta p )/(B)`
`implies V = v _(0) [ 1- (Delta p )/(B)]`
`therefore` Density, `rho = rho _(0) [ 1- (Delta p )/(B) ]^(-1) = rho _(0) [ 1 + (Delta p)/(B)]`
where, `Delta p= p - p _(0) = h rho _(0) g `
= pressure difference between depth and surface of ocean
` therefore rho = rho _(0) [1 + (rho _(0) g y )/(B) ]` (As h =y )