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)`

Explanation

Here, mass m=45 kg , height of leg bone h=2 m
Length L=0.50 m , Area of bones A`=5xx10^(-4)m^(2)`
Loss in gravitational energy =gain in elastic energy in both leg bones
So, `mgh=2xx((1)/(2)xx"stress"xx"strain"xx"volume")`
Here, volume `=AL=5xx10^(-4)xx0.50=2.5xx10^(-4)m^(3)`
`therefore 45xx10xx2=2xx[(1)/(2)xx0.9xx10^(8)xx2.5xx"strain"xx10^(-4)]`
or strain `=(45xx10xx2)/(0.9xx2.5xx10^(4))=0.04`
`therefore `Young's modulus of bones material
`Y=("Stress")/("Strain")=(0.9xx10^(8))/(0.04)=2.25xx10^(9) Nm^(-2)`