Thermal Expansion of Liquid Column

Steps:

• Initial length at 0°C: 2.0 cm.
• Total expansion from 0°C to 100°C: 10.0 cm over 100°C rise.
• Expansion rate: 10.0 cm / 100°C = 0.1 cm/°C.
• At 30°C, expansion = 0.1 cm/°C × 30°C = 3.0 cm; total length = 2.0 cm + 3.0 cm = 5.0 cm.

Why C is correct:

• Linear thermal expansion assumes uniform expansion proportional to temperature change, per the formula ΔL = L₀ α ΔT (here, effective α derived from given data).

Why the others are wrong:

• A: Underestimates expansion (only 0.3 cm added, ignoring full rate).
• B: Assumes uniform 1 cm per 10°C without initial length.
• D: Overestimates by adding full expansion scaled incorrectly.

Final answer: C