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)`

Answer

144.6 J

Explanation

Here, `A = 5 cm^2 = 5xx 10^(-4) m^2`, length of both the legs,
`l = 2xx 50 = 100 cm = 1.0 m` Limiting stress ` = 0.9 xx 10^8 Nm^(-2),`
`Y = 1.4 xx 10^(10) N m^(-2)`
Elastic potential energy. `U = (1)/(2)xx((stress)^2)/(Y) xx volume `
` = (1)/(2)xx((0.9xx 10^8)^2)/(1.4 xx 10^(10))xx(5xx10^(-4) xx 1.0) = 144.6 J`