B

Step 1: Convert the speed from km/hr to m/s.
Speed = 48 km/hr = \frac{48 \times 1000}{3600} = 13.33 \text{ m/s}.

Step 2: Use the formula for the cant (height difference) of rails in curves:
\[ h = \frac{v^2}{g r} \]
where:
- $h$ = height difference between the outer and inner rails
- $v$ = speed of the train = 13.33 m/s
- $g$ = acceleration due to gravity = 9.81 m/s²
- $r$ = radius of the curve = 400 m.

Step 3: Substitute the values into the formula:
\[ h = \frac{(13.33)^2}{9.81 \times 400} \]
\[ h = \frac{177.6889}{3920} \approx 0.0452 \text{ m} \approx 4.52 ext{ cm} \]

Step 4: Rounding the value to suitable precision, the height to raise the outer rail is approximately 4.5 cm.

Therefore, the correct answer is option B.