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Elastic Modulie

Question

A 40 kg boy whose leg are 4 ${cm}^{2}$ in area and 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can stand a stress of $1.0 \times 10^{8} N / m^{2}$ , calculate the Young's modulus for the material of the bone.

Moderate

A

$25 \times 10^{9} N / m^{2}$
B

$2.5 \times 10^{9} N / m^{2}$
C

$5.0 \times 10^{9} N / m^{2}$
D

none of these

Solution

Loss in gravitational energy = gain in elastic energy in both leg bones.
i.e., mgh = $2 \times (\frac{1}{2} \times stress \times strain \times volume)$
Here volume
= AL = $4 \times 10^{4} \times 0.5 = 2 \times 10^{- 4} m^{3}$
$40 \times 10 \times 2 = 1.0 \times 10^{8} \times strain \times 2 \times 10^{- 4}$
Strain = $\frac{40 \times 10}{1.0 \times 10^{4}} = 4 \times 10^{- 2}$
$Y = \frac{stress}{strain} = \frac{1.0 \times 10^{8}}{4 \times 10^{- 2}} = 2.5 \times 10^{9} N / m^{2}$

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