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, `m=45 kg, h=2m`,
`L=0.50 m: A = 5 xx 10^(-4)m^(2)`
Loss in gravitational energy = gain in elastic energy in both leg bones
so, `mgh = 2 xx [ 1/2 xx strai n xx strai n xx strai n xx volume]`
Here, volume `=AL=5 xx 10^(-4) xx 0.50`
`=2.5 xx 10^(-4) m^(3)`
`:. 45 xx 10 xx 2 `
`=2 xx [1/2 xx 0.9 xx 10^(8) xx strai n xx 2.5 xx 10^(-4)]`
or `strai n = (45 xx 10 xx 2)/(0.9 xx 2.5 xx 10^(4)) = 0.04`
`:. Y=(stress)/(strai n) = ( 0.9 xx 10^(8))/(0.04)`
`= 2.25 xx 10^(9) Nm^(-2)`.