Question

Young’s moduli of two wires $A$ and $B$ are in the ratio $7:4$. Wire $A$ is $2m$ long and has radius $R$. Wire $B$ is $1.5m$ long and has radius $2mm$. If the two wires stretch by the same length for a given load, then the value of $R$ is close to

• A. $1.3mm$
• B. $1.9mm$
• C. $1.5mm$
• D. $1.7mm$

Answer 1

The correct option is D $1.7mm$

Formula used: $\frac{\Delta l}{l}=\frac{F}{AY}$

Given: $\frac{Y_A}{Y_B}=\frac{7}{4},L_A=2m,A_A=\pi R^2,L_B=1.5m,r_B=2mm$

$\frac{F}{l}=Y\left(\frac{A}{L}\right)$

given $F$ and $l$ are same, $\frac{AY}{L}$ is same

$\frac{A_A{Y}_A}{L_A}=\frac{A_B{Y}_B}{L_B}$

$\frac{\left(\pi R^2\right)\left(\frac{7}{4}{Y}_B\right)}{2}=\frac{\pi (2{)}^2\cdot Y_B}{1.5}$

$R=1.74mm$

FINAL ANSWER: (b)