Question

What is the least radius of curve on a horizontal road, at which a vehicle can travel with a speed of $36\ \text{km/h}$ at an angle of inclination $45^\circ$? $\left[g = 10\ \text{m/s}^2,\ \tan 45^\circ = 1\right]$

• A. $10\ \text{m}$
• B. $20\ \text{m}$
• C. $25\ \text{m}$
• D. $15\ \text{m}$

Hint:

For minimum radius on a banked road, use $\tan\theta = \dfrac{v^2}{rg}$.

Answer 1

The Correct Option is A

Step 1: Convert speed into m/s.
\[ 36\ \text{km/h} = 10\ \text{m/s} \] Step 2: Use formula for banking of roads.
\[ \tan\theta = \dfrac{v^2}{rg} \] Step 3: Substitute given values.
\[ 1 = \dfrac{(10)^2}{r \times 10} \] Step 4: Solve for radius $r$.
\[ r = 10\ \text{m} \]