A 45 kg boy whose leg bones are `5 cm^(2)` in area and 50 cm long falls through a height of 2m without breaking his leg bones. If the bones can stand a stress of `0.9 xx 10^(8) Nm^(-2)`, then young's modulus for the material of the bone 18

Options

A. `2.25 xx 10^(7) Nm^(-2)`
B. `2.25 xx 10^(9) Nm^(-2)`
C. `8.5 xx 10^(7) Nm^(-2)`
D. `8.85 xx 10^(9) Nm^(-2)`

Answer

c

Explanation

Here, m = 45 kg, h = 3 m, L = 0.5 m, `A = 5 xx 10^(4) m^(2)`
Less in gravitional energy = gain in elastic energy in both leg bones.
`implies mgh = 2 xx ((1)/(2) xx "stress" xx "strain" 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 "strain" xx 2.5 xx 10^(-4))`
`implies "strain" = (45 xx 10 xx 2)/(0.9 xx 2.5 xx 10^(4)) = 0.04`
`:. 45 xx 10 xx 2 = 2 xx ((1)/(2) xx 0.9 xx 10^(8) xx "sttain" xx 2.5 xx 10^(-4))`
`implies = ("stress")/("strain") = (0.9 xx 10^(8))/(0.04)`
`y = 2.25 xx 10^(9) Nm^(-2)`