Question

To what depth must a rubber ball be taken in deep sea so that it's volume is decreased by 0.1%. ( Bulk modules of rubber is 9.8 x 10 to the power 8 N/m square . and the density of seawater is 10 to the power of 3 kg/m cube?

Answer 1

Hi

Here is your answer,

Bulk modules of rubber (B) = 9.8 × 10⁸ N/m²

Density of sea water (ρ) = 10³ kg/m³ 

Percentage decreases in volume ,

       ( ΔV/V × 100 ) = 0.1 or ΔV/V = 0.1 / 100

   OR ,        ΔV/V = 1/1000

  Let the rubber ball be taken up to depth h.


 ∵ Change in pressure (p) = hρg

 ∴ Bulk modules (B) = p/(ΔV/V) = hρg/(ΔV/V) 

OR ,         h = B × (ΔV/V)/ρg = 9.8 × 10⁸ × 1/1000/10³ × 9.8 = 100m



Hope it helps you !