A 40 kg boy whose leg are `4cm^2` in area and `50cm` long falls through a height of `2m` without breaking his leg bones. If the bones can stand a stress of `1.0xx10^8(N)/(m^2)`, calculate the Young's modulus for the material of the bone.

Explanation

`Mass = 40kg`, area of each leg `= 4 cm^(2) = 4xx10^(-4) m^(2)` breaking stress `= 0.9xx10^(8) N//m^(2)`,
length of each leg `= 50cm = 50xx10^(-2) m`.
From `E = (1)/(2) xx (("stress"))/(Y) xx A xx L`
Where elastic energy of bone in the form of potential energy, `E = mgh`, For two legs,
`mgh = 2[(1)/(2) xx ("stress"^(2))/(Y) xx "volume".]`,
`Y = ((0.9xx10^(8))^(2) xx 4xx10^(-4) xx 50xx10^(-2))/(40xx9.8xx2)`
`= 2.05xx10^(9) N//m^(2)`