Correct Answer: Option C

Explanation

For Hooke's law F = Ke

\( \implies \frac{F}{e} = K\)

\(\frac{f_1}{e_1} = \frac{f_2}{e_2}\)

\(\text{Let the original length} = t_0 \)

\(\text{therefore}\) e\(_1\) = (36 - t_0)\)cm ; e\(_2 = (46 - t_0)\)cm 
\(f_1\) = 40N, \(f_2\) = 60N
\(\frac{40}{36 - t_0} = \frac{60}{45 - t_0}\)
\(\implies 40(45 - t_0) = 60(36 - t_0)\)
\(\text{therefore } 1800 - 40t_0\) = 2160 - 60\(t_0\)
60\(t_0\) - 40\(t_0\) = 2160 - 1800
20\(t_0\) = 360
\(t_0\) = 18cm

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