Q21 of 29 Page 69

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8×108 N m-2; and the density of sea water is 103 kg m-3.)

Water density is 103 kg m-3.


We know that Bulk Modulus is given by



Where,


Change in pressure (indirectly implies change in force around the solid which is under observation)


Change in volume of solid due to change in pressure.


Intial Volume of solid


Let assume that Pressure outside sea is and to a depth h the pressure is equal to



Therefore,



Where,


Change in pressure as we are going below sea level


Density of water


=height from sea level


Now it is given that volume decrease percentage which is equal to 0.1%.



And Bulk Modulus is 9.8×108 N m-2 with sea water density equal to 103 kg m-3.Therefore putting values in equation 1, we get



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