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 is2.2 xx 10 ^(9) Nm ^(-2) ("Take" g = 10 ms ^(-2))

The average depth of Indian Ocean is about 3000 m. Calculate the fract

1.	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 is2.2 xx 10 ^(9) Nm ^(-2) ("Take" g = 10 ms ^(-2))
Answer» Solution :`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 %`