Q128 / 150 · MHT CET 2020 (14 Oct Shift 1) · Physics

Two wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the second overtone of second wire and radius of first wire is twice the radius of the second then the ratio of length of first wire to second wire is

  • Correct answer
    A
    $1: 3$
  • B
    $1: 2$
  • C
    $2: 1$
  • D
    $3: 1$

Solution

$\mathrm{n}_{1}=2 \cdot \frac{1}{2 \ell_{1} \mathrm{r}_{1}} \sqrt{\frac{\mathrm{T}}{\pi \rho}} ; \mathrm{n}_{2}=3 \cdot \frac{1}{2 \ell_{2} \mathrm{r}_{2}} \sqrt{\frac{\mathrm{T}}{\pi \rho}}$ $\mathrm{n}_{1}=\mathrm{n}_{2} \quad \therefore \frac{2}{\ell_{1} \mathrm{r}_{1}}=\frac{3}{\ell_{2} \mathrm{r}_{2}} \quad \therefore \frac{\ell_{1}}{\ell_{2}} \quad=\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}} \times \frac{2}{3}=\frac{1}{2} \times \frac{2}{3}=\frac{1}{3}$

Hence, the correct answer is option: 'A'.

Relevant Questions