Question

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

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

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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