First slide

Elastic Modulie

Question

The bulk modulus of rubber is 9.1 x 10⁸ N/m². To what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1%?

Moderate

A

1km
B

85m
C

93m
D

110 m

Solution

We know that
$\begin{array}{l} B = \frac{PV}{ΔV} where P = hρg = h \times 10^{3} \times 9 \cdot 8 \\ \frac{ΔV}{V} = 0 \cdot 1 % = \frac{0 \cdot 1}{100} = 0 \cdot 1 \times 10^{- 2} \\ B = 9 \cdot 1 \times 10^{8} N / m^{2} \\ ∴ 9 \cdot 1 \times 10^{8} = \frac{h \times 10^{3} \times 9 \cdot 8}{0 \cdot 1 \times 10^{- 2}} \\ h \approx 100 m \end{array}$

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