In a metre-bridge when a resistance in the left gap is $2\ \Omega$ and unknown resistance in the right gap, the balance length is found to be $40\ \mathrm{~cm}$. On shunting the unknown resistance with $2\ \Omega$, the balance length changes by :
JEE MAIN 2024, Diffcult
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First case $\frac{2}{40}=\frac{X}{60} \Rightarrow X=3 \Omega$
In second case $X^{\prime}=\frac{2 \times 3}{2+3}=1.2 \Omega$
$\frac{2}{\ell}=\frac{1.2}{100-\ell}$
$200-2 \ell=1.2 \ell$
$\ell=\frac{200}{3.2}=62 . \mathrm{bm}$
Balance length changes by $22.5 \mathrm{~cm}$
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