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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.)
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Solution
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
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