Question

A ball falling in a lake of depth 300 m shows a decrease of 0.3% in its volume at the bottom. What is the bulk modulus of the material of the ball? (g = 10 m/s²)

Options

• 10⁶ N/m²

• 10⁹ N/m²

• 3 × 10² N/m²

• None

Answer 1

10⁹ N/m²

Explanation:

B = `"P"/((Δ"V")/"V")`

P = hρg

= 300 × 10³ × 10

= 3 × 10⁶ N/m²

`(Δ"V")/"V"` = 0.3%

= `0.3/100`

= 3 × 10⁻³ 

∴ B = `(3 xx 10^6)/(3 xx 10^-3)` = 10⁹ N/m²