1. Condition for banking of railway track

For a train moving on a curved track, the required cant (height difference) $h$ between the outer and inner rails is given by

$an\theta = \frac{v^2}{rg}$

If the rails are separated by distance $d$, then for small angle $\theta$,

$\tan\theta \approx \frac{h}{d}$

So,

$\frac{h}{d} = \frac{v^2}{rg}$

Hence,

$h = d\,\frac{v^2}{rg}$

2. Substitute the given values

Given:

• $v = 12\,\text{m/s}$
• $d = 1.5\,\text{m}$
• $r = 400\,\text{m}$
• $g = 10\,\text{m/s}^2$

Therefore,

$h = 1.5\times \frac{12^2}{400\times 10}$

$h = 1.5\times \frac{144}{4000}$

$h = 1.5\times 0.036$

$h = 0.054\,\text{m}$

3. Convert into cm

$0.054\,\text{m} = 5.4\,\text{cm}$

4. Match with the options

Thus, the required height difference is

$\boxed{5.4\,\text{cm}}$

So the correct option is B.