Q: A 40 kg boy whose legs are 4 cm^{2} in area 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can withstand a stress of 0.9 × 10^{8} N/m^{2}. Calculate the Young’s modulus of material of the bone.

Sol: Mass = 40 kg, area of each leg = 4 cm^{2} = 4 × 10^{-4} m^{2}

breaking stress = 0.9×10^{8} N/m^{2} ,

length of each leg = 50 cm = 50 × 10^{-2} m

As $\large U = \frac{1}{2}\times Stress \times Strain \times Volume $

$\large U = \frac{1}{2}\times Stress \times \frac{Stress}{Y} \times Volume $

where elastic energy of bone in the form of potential energy, U = m g h;

For two legs,

$\large m g h = 2 (\frac{1}{2}\times Stress \times \frac{Stress}{Y} \times Volume ) $

On Putting the given values , we get

Y = 2.05 × 10^{9} N/m^{2}