Question

When a tension $F$ is applied, the elongation produced in uniform wire of length $L$, radius $r$ is $e$. When tension $2F$ is applied, the elongation produced in another uniform wire of length $2L$ and radius $2r$ made of same material is:

• A. $0.5e$
• B. $1.0e$
• C. $1.5e$
• D. $2.0e$

Answer 1

Answer: (B)

$1.0e$

$Y=\frac{F/\pi r^2}{△l/l}$

$△l=\frac{Fl}{\pi r^{2}Y}$

$E=\frac{Fl}{\pi r^{2}Y}-------1$

$△l=\frac{2F2l}{\pi 4r^{2}Y}$

$△l=\frac{Fl}{\pi r^{2}Y}=e$ ---------- (By 1)

=> elongation is none wire is same as $e$