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A 45 kg boy whose leg bones are 5 cm^(2)...

A 45 kg boy whose leg bones are `5 cm^(2)` in area and 50 cm long falls through a height of 2m with out breaking his leg bones. If the bones can stand a stress of `0.9 xx 10^(8) Nm^(-2)`, Calculate the Young's modulus for the material of the bone. Use , `g=10 ms^(-2)`

Text Solution

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Here, m = 45 kg, h = 2 m, L = 0.50 m, A = `5xx10^(-4)m^(2)`
Loss in gravitational potential energy = gain in elastic potential energy in both leg bones
So, `mgh=2xx((1)/(2)"Stress"xx"strain"xx"volume")`
`therefore" "45xx10xx2=2xx[(1)/(2)xx0.9xx10^(8)xx"strain"xx2.5xx10^(-4)]`
Strain = 0.04
`therefore" "Y=("Stress")/("Strain")=(0.9xx10^(8))/(0.04)=2.25xx10^(9)Nm^(-2)`
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