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The average depth of Indian Ocean is about $$3000m$$. The fractional compression, $$\cfrac { \Delta V }{ V } $$ of water at the bottom of the ocean is then
(Given: Bulk modulus of the water$$=2.2\times { 10 }^{ 9 }N{ m }^{ -2 }$$ and $$g=10m{ s }^{ -2 }$$)


A
0.82%
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B
0.91%
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C
1.36%
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D
1.24%
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Solution

The correct option is C $$1.36$$%
The pressure exerted by a $$3000m$$ column of water on the bottom layer is
$$P=h\rho g=3000m\times 1000kg\quad { m }^{ -3 }\times 10m\quad { s }^{ -2 }=3\times { 10 }^{ 7 }N\quad { m }^{ -2 }\quad $$
Fractional compression $$\cfrac { \Delta V }{ V } $$ is
$$\cfrac { \Delta V }{ V } =\cfrac { P }{ B } =\cfrac { 3\times { 10 }^{ 7 }N\quad { m }^{ -2 } }{ 2.2\times { 10 }^{ 9 }N\quad { m }^{ -2 } } =1.36\times { 10 }^{ -2 }=1.36\quad $$%

Physics

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