A metallic wire of resistance R and resistivity ρ is cut into six equal parts. Now each part is stretched to six times its length. The new resistance and resistivity of each part will be, respectively:

6 R and ρ

The correct answer is Option (3) → 6 R and ρ

Resistance of original wire (R) and Resistivity (ρ)

$R_{part}$ (cut into 6 equal pieces) = $\frac{R}{6}$

Also, each part is stressed six times its length -

$L_{new}=6×\frac{L}{6}=L$

$A_{new}=\frac{original\,volume}{New\,length}=\frac{A.\frac{L}{6}}{L}=\frac{A}{6}$

$R_{new}=ρ\frac{L}{A_{new}}=6$

$\frac{ρL}{A}=6R$

Also,

Resistivity (ρ) is a material property and does not change with dimension.