For traffic moving at 60 km / hr along a circular track of radius 0.1 km , the correct angle of banking is

The correct option is: tan⁻¹[(50/3)²/100x9.8]

Step-by-Step Derivation:

For any vehicle moving along a circular track of radius r at a constant speed v, the optimum angle of banking
$\theta$
without relying on friction is given by the formula:
$tan\theta =\frac{v^2}{rg}$
where g is the acceleration due to gravity.

Let us convert the given values into standard SI units:

1. Speed of the traffic (v):
$v=60\text{km/hr}$
To convert kilometers per hour to meters per second, we multiply by
$\frac{5}{18}$

$v=60\times \frac{5}{18}=\frac{50}{3}\text{m/s}$

2. Radius of the circular track (r):
$r=0.1\text{km}$
Converting kilometers to meters:
$r=0.1\times 1000=100\text{m}$

3. Acceleration due to gravity (g):
$g=9.8{\text{m/s}}^2$

Substituting these values back into the banking angle formula:
$tan\theta =\frac{{\left(\frac{50}{3}\right)}^2}{100\times 9.8}$

Solving for
$\theta$
by taking the inverse tangent of both sides:
$\theta ={tan}^{-1}\left[\frac{{\left(\frac{50}{3}\right)}^2}{100\times 9.8}\right]$

Therefore, the correct banking angle is: tan⁻¹[(50/3)²/100x9.8].