Question

2 A 40 kg boy whose legs are 4 cm in area and 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can withstand stress of 0.9 x 10⁸ N/m². The Young's modulus for the material of the bone is ______.

Options

• 0.9 × 10⁸ N/m²

• 5 × 10⁸ N/m²

• 2.05 × 10⁹ N/m²

• 2.05 × 10⁸ N/m²

Answer 1

2 A 40 kg boy whose legs are 4 cm in area and 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can withstand stress of 0.9 × 10⁸ NI m². The Young's modulus for the material of the bone is 2.05 × 10⁹ N/m².

Explanation:

Loss in gravitational energy = gain in stress - strain

energy i.e., mgh = `1/2`(stress × strain × volume) × 2

`=> "Y" = (("stress")^2 xx "volume")/"mgh"`

`= ((1 xx 10^8)^2 xx 4 xx 50 xx 10^-6)/(40 xx 10 xx 2) = 2.05 xx 10^9`N/m²