Question

If the ratio of radii of two wires of same material is $3: 1$ and ratio of their lengths is $5: 1$, then the ratio of the normal forces that will produce the same extension in the length of two wires is

• A. $2: 1$
• B. $4: 1$
• C. $1: 4$
• D. $1: 1$

Answer 1

Answer: (D)

$Y =\frac{ F \ell}{ A \Delta \ell} ; \Rightarrow F =\frac{ YA \Delta \ell}{\ell}$
$\frac{F_1}{F_2}=\frac{A_1}{A_2} \times \frac{l_2}{l_1}$
$=\frac{r_1^2}{r_2^2} \times \frac{l_2}{l_1}=\frac{4}{1} \times \frac{1}{4}=1: 1 .$