Question

A car is moving in a circular path of radius \(20\,m\) with speed \(54\,km/hr\). A pendulum is hanging from the roof of the car. Find the angle made by pendulum with vertical. (Take \(g=10\,m/s^2\)).

• A. \( \tan^{-1}\left(\frac{9}{8}\right) \)
• B. \( \tan^{-1}\left(\frac{8}{9}\right) \)
• C. \( \tan^{-1}\left(\frac{4}{3}\right) \)
• D. \( \tan^{-1}\left(\frac{3}{4}\right) \)

Answer 1

The Correct Option is A

Concept: When a car moves in a circular path, the pendulum experiences a horizontal pseudo force due to centripetal acceleration.

Resolving forces on the bob: \[ T\cos\theta = mg \] \[ T\sin\theta = \frac{mv^2}{r} \] Dividing the two equations, \[ \tan\theta = \frac{v^2}{rg} \]
Step 1:Convert speed into SI units. \[ v = 54 \times \frac{5}{18} \] \[ v = 15\,m/s \]
Step 2:Substitute values in the equation. \[ \tan\theta = \frac{v^2}{rg} \] \[ \tan\theta = \frac{15^2}{20 \times 10} \] \[ \tan\theta = \frac{225}{200} \] \[ \tan\theta = \frac{9}{8} \] \[ \boxed{\theta = \tan^{-1}\left(\frac{9}{8}\right)} \]