If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η the Poisson ratio σ will be

Question

If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η the Poisson ratio σ will be (A)  +(2/3)  (B)  -(1/4)  (C)  +(1/4)  (D)  -(2/3)

Tardigrade Admin · Accepted Answer

Young's modulus, Y=(3η /2) We know that Y=2η (1+σ ) ∴ (3η /2)=2η (1+σ ) ⇒ σ =-(1/4)

Q. If Young's modulus of elasticity $Y$ for a material is one and half times its rigidity coefficient $η$ the Poisson ratio $σ$ will be

$+ \frac{2}{3}$

$- \frac{1}{4}$

$+ \frac{1}{4}$

$- \frac{2}{3}$

Young's modulus, $Y = \frac{3 η}{2}$
We know that $Y = 2 η (1 + σ)$
$∴$ $\frac{3 η}{2} = 2 η (1 + σ)$
$\Rightarrow$ $σ = - \frac{1}{4}$

Q. If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η the Poisson ratio σ will be

+32​

−41​

+41​

−32​