A uniform solid cylindrical rod is subjected to a longitudinal...

Poisson's ratio ($\sigma$) is defined as the ratio of lateral strain to longitudinal strain.

The longitudinal strain is the fractional change in length:
Longitudinal strain $= \dfrac{\Delta L}{L} = \dfrac{0.1}{100} = 0.001$

The lateral strain is the fractional change in diameter (considering magnitude):
Lateral strain $= \dfrac{\Delta d}{d} = \dfrac{0.03}{100} = 0.0003$

Poisson's ratio is given by:
$\sigma = \dfrac{\text{Lateral strain}}{\text{Longitudinal strain}} = \dfrac{0.0003}{0.001} = 0.3$

Alternatively, using percentage changes directly:
$\sigma = \dfrac{0.03\%}{0.1\%} = 0.3$

Answer: $0.3$