The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If YA and YB are the Youngs modulus of the materials, then:

Question

The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If YA and YB are the Youngs modulus of the materials, then: (A)  YB=2YA  (B)  YA=YB  (C)  YB=3YA  (D)  YA=3YB

Tardigrade Admin · Accepted Answer

Y=(stress/strain)= slope of the graph = tan θ ∴ (YA/YB)=( tan 60° / tan 30° )=(√3/1/√3)=3 ⇒ YA=3YB

Q. The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If $Y_{A}$ and $Y_{B}$ are the Youngs modulus of the materials, then:

$Y_{B} = 2 Y_{A}$

$Y_{A} = Y_{B}$

$Y_{B} = 3 Y_{A}$

$Y_{A} = 3 Y_{B}$

$Y_{B} = \frac{1}{3} Y_{A}$

$Y = \frac{s t ress}{s t r ain} =$ slope of the graph
$= tan θ$
$∴$ $\frac{Y _{A}}{Y _{B}} = \frac{t a n 60 ^{\circ}}{t a n 30 ^{\circ}} = \frac{3}{1/ 3} = 3$
$\Rightarrow$ $Y_{A} = 3 Y_{B}$

Q. The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If YA​ and YB​ are the Youngs modulus of the materials, then:

YB​=2YA​

YA​=YB​

YB​=3YA​

YA​=3YB​

YB​=31​YA​

Y=strainstress​= slope of the graph =tanθ ∴ YB​YA​​=tan30∘tan60∘​=1/3​3​​=3 ⇒ YA​=3YB​