Q174 / 180 · KCET 2008 · Physics

A string vibrates with a frequency of $200 \mathrm{~Hz}$. When its length is doubled and tension is altered, it begins to vibrate with a frequency of $300 \mathrm{~Hz}$. The ratio of the new tension to the original tension is

  • Correct answer
    A
    $9: 1$
  • B
    $1: 9$
  • C
    $3: 1$
  • D
    $1: 3$

Solution

$\quad v=\frac{1}{2 l} \sqrt{\frac{\mathrm{T}}{\mathrm{m}}}$ $\Rightarrow \quad v \propto \frac{\sqrt{\mathrm{T}}}{1}$ $\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\left[\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}\right]^{2}\left[\frac{\mathrm{l}_{2}}{\mathrm{l}_{1}}\right]^{2}=\left[\frac{300}{200}\right]^{2}\left[\frac{21}{\mathrm{l}}\right]^{2}=\frac{9}{1}$

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

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