First slide

Elastic behaviour of solids

Question

If a rubber cube is taken 50 m deep in a lake, its volume reduces by 0.5%. The bulk modulus of rubber is nearly.

Moderate

A

$10^{6} Pa$
B

$10^{7} Pa$
C

$10^{8} Pa$
D

$10^{9} Pa$

Solution

Excess pressure at depth h = 50 m is
$P = hρg = 50 \times 1000 \times 9 .8 = 4 .9 \times 10^{5} Pa$
Volume strain $\frac{ΔV}{V} = - 0 .5 % = - 0 .5 \times 10^{- 2}$
$∴$ Bulk modulus $= - \frac{P}{\frac{ΔV}{V}} = - \frac{4 .9 \times 10^{5}}{- 0 .5 \times 10^{- 2}} ≃ 10^{8} Pa$
So the correct choice is (c).

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