Question

Two wires of same material and radii $r$ and $2r$ respectively are welded together end to end. The combination is used as a sonometer wire under tension $T$. If the welded point lies midway, then the ratio of the number of loops formed in thinner and thicker wire is

• A. $1:2$
• B. $2:1$
• C. $1:3$
• D. $3:1$

Answer 1

Answer: (A)

$1:2$

$f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}=\frac{1}{2l}\sqrt{\frac{T}{\delta \left(A\right)}}$
$\Rightarrow \frac{f_1}{f_2}=\sqrt{\frac{A_2}{A_1}}=\sqrt{(2{)}^2}=2$
Number of loops $\propto \lambda \propto \frac{1}{f}$
$\therefore \frac{n_1}{n_2}=\frac{1}{2}$