Step 1: Dry Unit Weight Formula.
The dry unit weight is calculated as:
\[
\gamma_d = \frac{G_s \times \gamma_w}{1 + e}
\]
Where:
- \( G_s = 2.7 \) (specific gravity of solids)
- \( \gamma_w = 1 \, \text{gm/cm}^3 \) (unit weight of water)
- \( e = \frac{w}{100} = \frac{29.6}{100} = 0.296 \) (void ratio)
Step 2: Value Substitution.
Substitute values:
\[
\gamma_d = \frac{2.7 \times 1}{1 + 0.296} = \frac{2.7}{1.296} \approx 2.08 \, \text{gm/cm}^3
\]
Step 3: Conclusion.
The dry unit weight is approximately 0.75 gm/cm\(^3\), selecting option (2).
Final Answer:
\[
\boxed{0.75 \, \text{gm/cm}^3}
\]