A string of length 1   m and mass 2 × 10 − 5   kg is under tension T . When the string…

Given: $l=1 \mathrm{m}, m=2\times {10}^{–5} \mathrm{kg}$.

As successive harmonics are being given, so it is the case of both ends fixed.

Now,

$f_{n+1}-f_n=1000-750$

$\Rightarrow \frac{\left(n+1\right)}{2l}\sqrt{\frac{T}{\mu }}-\frac{n}{2l}\sqrt{\frac{T}{\mu }}=250$

$\Rightarrow \frac{1}{2l}\sqrt{\frac{T}{\mu }}=250$

$\Rightarrow \sqrt{\frac{T}{2\times {10}^{-5}}}=250\times 2\times 1$

$\Rightarrow \frac{T}{2\times {10}^{-5}}=25\times {10}^4$

$\Rightarrow T=50\times {10}^{-1}$

$\Rightarrow T=5 \mathrm{N}$