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Question

A boy of mass 45 kg, whose leg bones have a cross-sectional area of 5 cm2 and length 50 cm, falls through a height of 2 m without breaking his leg bones. If the bones can withstand a stress of 0.9×108 Nm2, calculate the Young's modulus for the material of the bone. Use, g=10 ms2

A
9×109 N m2
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B
4.5×109 N m2
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C
2.25×109 N m2
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D
1.2×109 N m2
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Solution

The correct option is C 2.25×109 N m2
Here,
m=45 kg, h=2 m;
L=0.50 m,A=5×104 m2

Using conservation of energy,
Loss in gravitational energy = gain in elastic energy in both leg bones
i.e mgh=2×[12×stress×strain×volume]
Here, volume=A×L=5×104×0.50=2.5×104 m3

45×10×2=2×[12×0.9×108×strain×2.5×104]
[using maximum permissible stress]
or Strain =45×10×20.9×2.5×104=0.04

Y=stressstrain=0.9×1080.04

Y=2.25×109 Nm2

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