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Question

The relation between Young's modulus $$Y$$, bulk modulus $$K$$ and modulus of elasticity $$\sigma$$ is


A
1y=1k+3η
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B
3y=1η+13k
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C
1y=3η+13k
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D
1η=3y+13k
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Solution

The correct option is B $$\cfrac { 3 }{ y } =\cfrac { 1 }{ \eta } +\cfrac { 1 }{ 3k } $$
We know that,
$$Y=3K(1-2\sigma)$$
or, $$\sigma=\dfrac{1}{2}(1-\dfrac{Y}{2K})$$ ----------(i)
Also, $$Y=2\eta(1+\sigma)$$
or, $$\sigma=\dfrac{Y}{2\eta}-1$$ ----------(ii)
Now, From (i) and (ii),
$$\dfrac{1}{2}(1-\dfrac{Y}{3K})=\dfrac{Y}{2\eta}-1$$
or, $$1-\dfrac{Y}{3K}=\dfrac{Y}{\eta}-2$$
or, $$\dfrac{3}{Y}=\dfrac{1}{\eta}+\dfrac{1}{3K}$$

Physics

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