Question

A car moves at a speed of \( 20 { m/s} \) on a banked track and describes an arc of a circle of radius \( 40\sqrt{3} \) m. The angle of banking is: (Take \( g = 10 { m/s}^2 \))

• A. \( 25^\circ \)
• B. \( 60^\circ \)
• C. \( 45^\circ \)
• D. \( 30^\circ \)

Hint:

For banking problems:
- The equation \( \tan \theta = \frac{v^2}{g R} \) determines the angle.
- No friction is needed if speed matches the ideal banking angle.

Answer 1

The Correct Option is D

Step 1: Use the banking formula
The angle of banking is given by:
\[ \tan \theta = \frac{v^2}{g R} \]
Step 2: Substitute given values
\[ \tan \theta = \frac{(20)^2}{(10) (40\sqrt{3})} \]
\[ \tan \theta = \frac{400}{400\sqrt{3}} \]
Step 3: Solve for \( \theta \)
\[ \tan \theta = \frac{1}{\sqrt{3}} \]
- Since \( \tan 30^\circ = \frac{1}{\sqrt{3}} \), we get:
\[ \theta = 30^\circ \]