If Youngs modulus of elasticity Y for a material is one and half times its rigidity coefficient n , the Poisson ratio a will be

Question

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

Tardigrade Admin · Accepted Answer

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

Q. If Youngs modulus of elasticity $Y$ for a material is one and half times its rigidity coefficient $n$ , the Poisson ratio a will be

$+ \frac{2}{3}$

$- \frac{1}{4}$

$+ \frac{1}{4}$

$- \frac{1}{4}$

Youngs 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 Youngs modulus of elasticity Y for a material is one and half times its rigidity coefficient n , the Poisson ratio a will be

+32​

−41​

+41​

−41​

Youngs modulus, Y=23η​ We know that Y=2η(1+σ) ∴23η​=2η(1+σ) ⇒σ=−41​

Q. If Youngs modulus of elasticity $Y$ for a material is one and half times its rigidity coefficient $n$ , the Poisson ratio a will be

$+ \frac{2}{3}$

$- \frac{1}{4}$

$+ \frac{1}{4}$

$- \frac{1}{4}$

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