Initially, copper wire radius (r₁) = 9 mm

Resistance (R) = 14 $$\Omega$$

We know, $$R = {{\rho L} \over A} = {{\rho L} \over {\pi r_1^2}} = 14$$

Now this copper wire is replaced by 7 parallel copper wire of resistance R₁.

$$\therefore$$ Equivalent resistance of 7 parallel copper wire,

$${1 \over {{R_{eq}}}} = {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}} + {1 \over {{R_1}}}$$

$$ \Rightarrow {1 \over {{R_{eq}}}} = {7 \over {{R_1}}}$$

$$ \Rightarrow {R_{eq}} = {{{R_1}} \over 7}$$

$$ = {1 \over 7} \times {{\rho L} \over {\pi r_2^2}}$$

$$ = {1 \over 7} \times {{\rho L} \over {\pi {{\left( {{{{r_1}} \over 3}} \right)}^2}}}$$ [as $${r_2} = {{{r_1}} \over 3}$$ ; $${r_1} = 9$$ m and $${r_2} = 3$$]

$$ = {1 \over 7} \times {{\rho L} \over {\pi r_1^2}} \times 9$$

$$ = {1 \over 7} \times 14 \times 9$$

$$ = 18\,\Omega $$