A

Step 1: Analyze the system. The apparatus consists of two sections at 95ºC (A and C) and two sections at 5ºC (B and D). The heights of the liquid columns are as follows:
- Height in column A (h_A) = 52.8 cm
- Height in column D (h_D) = 51 cm

Step 2: Calculate the height difference due to thermal expansion. The equilibrium of the columns indicates that the heights are affected by temperature differences:
- Height difference due to temperature difference can be calculated using the formula:
$$h_A - h_D = ext{Coefficient of thermal expansion} imes (T_A - T_D) imes ext{length}$$
Where:
- $T_A = 95ºC$, $T_D = 5ºC$
- $h_A - h_D = 52.8 - 51 = 1.8 ext{ cm}$
- Length is the average height of the liquid column

Step 3: Since the columns B and C maintain equal temperature, we can use it to relate the thermal expansion. The average height (before thermal expansion) is approximately 49 cm (the heights of columns B and C). Using the average height, we compute the coefficient of thermal expansion ($eta$):
$$1.8 = eta imes (95 - 5) imes 49$$
Step 4: Rearranging the equation for coefficient:
$$eta = \frac{1.8}{(95 - 5) imes 49}$$
$$eta = \frac{1.8}{90 imes 49} = \frac{1.8}{4410} = 0.0004086 ext{ per } ^ ext{o}C$$
Step 5: Since this is a coefficient value, we usually express it in per degree Celsius, thus:
$$eta = 0.00041 ext{ per } ^ ext{o}C$$ (after rounding).
Therefore, the coefficient of thermal expansion of the liquid is approximately:
$$eta ext{ is in } A.$$