$(a)\;4 \times 10^{-4}\;S \\ (b)\;\frac{1}{2} \times 10^{-4}\;S \\(c)\;2 \times 10^{-4}\;S \\(d)\;1 \times 10^{-4}\;S $

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When a srteroid is cut it two parts the self inductance and resistance will become half.

$L$ for each part $ = \large\frac{8 \times 10^{-4}}{2} $$=4 \times 10^{-4}\;H$

R for each part $=2 \Omega$

When they are connected in parallel the effective inductance $L= \large\frac{4 \times 10^{-4}}{2}$

$\qquad= 2 \times 10^{-4}\;H$

effective $R=\large\frac{2}{2}$$ \;\Omega=1 \Omega$

The time constant $T= \large\frac{L}{R}$

$\qquad= \large\frac{2 \times 10^{-4}}{1}$

$\qquad= 2 \times 10^{-4}$

Hence c is the correct answer.

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