Question

A rubber ball is taken to depth 1 km inside water so that its volume reduces by 0.05%. What is the bulk modulus for rubber?

Answer 1

A rubber ball is taken 1 km depth inside water .
Pressure on rubber ball , P = P₀ + ρgh
Here, P₀ is atmospheric pressure ,ρ is density of water , g is acceleration due to gravity and h is depth inside water .

Given, h = 1 km = 1000 m
g = 10 m/s² , ρ = 1000 kg/m³ density of water ]
Now , pressure act on rubber ball , P = 1.03 × 10⁵ + 1000 × 10 × 1000
= 1.03 × 10⁵ + 100 × 10⁵ = 101.03 × 10⁵ N/m²

Given ∆V/V = 0.05/100 and ∆P = P - P₀ = 10⁷ N/m²[∵ volume reduced 0.05 % ]
∆V/V = 5 × 10⁻⁴

Now, bulk modulus = ∆P/∆V/V
= 10⁷/5 × 10⁻⁴
= 2 × 10¹⁰N/m²

Answer 2

this is what I can do the smallest and the simplest way.....