Question

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 Nm^–2; and the density of sea water is 10³ kg m^–3.)

Answer 1

Given the Bulk modulus of rubber (K) = 9.8 × 10⁸ N/m²

The density of seawater (ρ) = 103 kg/m3

Percentage decrease in volume, `((ΔV)/V xx 100)` = 0.1

⇒ `(ΔV)/V = 0.1/100`

⇒ `(ΔV)/V = 1/1000`

Let the rubber ball be taken up to depth h.

∴ Change in pressure (p) = hpg

∴ Bulk modulus `(K) = |p/((ΔV)/V)| = (hpg)/(((ΔV)/V))`

⇒ `h = (K xx ((ΔV)/V))/(pg)`

= `(9.8 xx 10^8xx 1/1000)/(10^3 xx 9.8)`

= 100 m