The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression, `Delta V` of water at the bottom of the ocean, given that the bulk modulus of water is`2.2 xx 10 ^(9) Nm ^(-2) ("Take" g = 10 ms ^(-2))`

Explanation

`h = 3000 m`
Density of water `rho = 10 ^(3) kgm ^(-3)`
Density of water `rho = 10^(3) kgm ^(-3)`
Gravitational acceleration `g = 10 ms ^(-2)`
`therefore` The pressure exerted on the bottom of ocean,
`P = h rho g`
`= 3 xx 10 ^(3) xx 10 ^(3) xx 10`
`("Force")/("Area") = 3 xx 10 ^(7) Nm ^(-2)`
Now bulk modulus,
`B= ("Stress")/("Volume strain") = ("Stress")/(Delta V //V)`
`therefore (Delta V)/(V) = ("Stress")/(B) `
`= (3 xx 10 ^(7))/( 2.2 xx 10 ^(9)) [because` Stress = Pressure P]
`= 1.36 xx 10 ^(-2)`
`therefore` Volume strain `= (Delta V)/(V) xx 100 %`
`= 1. 36 xx 10 ^(-2) xx 10 0 % = 1.36 %`