Question

A car moves at a speed of \(600\,\text{km/h}\) on a frictionless banked road with \(\theta=30^{\circ}\). Take \(g=10\,\text{m/s}^{2}\). Find the radius of the road.

• A. \(2.4\,\text{km}\)
• B. \(3.2\,\text{km}\)
• C. \(4.8\,\text{km}\)
• D. \(6.4\,\text{km}\)

Hint:

For a frictionless banked road, always use \[ \boxed{\tan\theta=\frac{v^{2}}{rg}} \] or equivalently, \[ \boxed{r=\frac{v^{2}}{g\tan\theta}}. \] Before substituting values, always convert the speed from km/h to m/s using \[ \boxed{1~\text{km/h}=\frac{5}{18}~\text{m/s}}. \] Also remember: \[ \boxed{\text{Higher speed } \Rightarrow \text{ Larger radius for the same banking angle}.} \]

Answer 1

The Correct Option is C

For a frictionless banked road, resolving forces gives $\tan\theta = v^2/(rg)$. With $v = 600$ km/h $\approx 166.7$ m/s, the required banking angle is found by substituting the given radius into this expression.