Question

Three wires P,Q and R the same materials and length have radii $0.12cm,0.2cm$ and $0.3cm$ respectively. Which wire has the highest value of Young's modules of elasticity ?

• A. P
• B. Q
• C. R
• D. All have the same value

Answer 1

The correct option is A P

We know Young's Modulus of elasticity $E=\frac{stress}{strain}$------(A)

Also we know stress $\sigma =\frac{F}{A}$where F and A are the force and area of cross section.

And strain $ϵ=\frac{l_0}{\Delta l}$ where $l_0$ and $\Delta L$ are the original length and elongation length.

Reducing the above found values of stress and strain in A we get,

$E=\frac{F{l}_0}{A\Delta l}$

Considering force applied in each wires to be same and given length of wires P,Q and R are same.

$E_P=\frac{F{l}_0}{0.12\Delta l_P}$-------(B)

$E_Q=\frac{F{l}_0}{0.2\Delta l_Q}$-------(C)

$E_R=\frac{F{l}_0}{0.3\Delta l_R}$ -------(D)

Now comparing equation B,C and D we can say

$E\alpha \frac{1}{A\Delta l}$

Thus we can say that wire P will have the highest Young's modulus of elasticity.