Question

For a given material,the rigidity modulas is (1/3)rd of Young's modulus.Its Poisson's ratio is____
A)0
B)0.25
C)0.3
0.5

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

For a given material,the rigidity modulas is ⅓rd of Young's modulus.Its Poisson's ratio ________

$\huge\underline{\underline{\bf \orange{Solution-}}}$

We know that :

✪$\large{\boxed{\bf \blue{Y=2\eta(1+\sigma)} }}$

Here $\eta$ = ⅓Y

$\implies{\sf Y = 2×\dfrac{1}{3}Y×(1+\sigma)}$

$\implies{\sf Y = \dfrac{2}{3}Y×(1+\sigma)}$

$\implies{\sf \dfrac{Y×3}{2×Y}=(1+\sigma)}$

$\implies{\sf \sigma=1-1.5}$

$\implies{\bf \red{Poison's\:ratio(\sigma)=0.5}}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Option (d) 0.5