Question

Modulus of rigidity and Bulk modulus of a wire are 4.55 x 1010 Nm-2 and 7.11 X 1010 Nm-2 respectively. Find its Young's modulus.

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Answer 1

Answer:

The modulus of rigidity and Bulk modulus of a wire are 4.55 x 1010 Nm-2 and 7.11 X 1010 Nm-2 respectively, its Young's modulus is $15*10^{10}N/m^{2}$

​Explanation:

• Bulk modulus ($K$)is the relative change in volume by unit tensile stress

• Young's modulus($Y$) is the ratio of stress to strain along the axial line

• Rigidity modulus(η) is the ratio of rigidity stress to corresponding strain
• The relation connecting the above three constants is

                           $3/Y=1/3K+$$1/$η

From the question, we have

modulus of rigidity η$=4.55*10^{10}N/m^{2}$

bulk modulus $K=7.11*10^{10}N/m^{2}$

The young's modulus can be calculated as

$3/Y=\frac{1}{3*4.55*10^{10} } +\frac{1}{7.11*10^{10} } =0.2*10^{-10}\\Y=\frac{3}{0.2*10^{-10} } =15*10^{10}N/m^{2}$