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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Circular Motion

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Circular Motion

A park has a radius of 10 m . Determine the proper angle of banking...

A park has a radius of

10 \text{ m}

. Determine the proper angle of banking if a vehicle travels around it at an average speed of

18 \text{ km/hr}

.

Options

A $\tan^{-1} \left(4\right)$
B $\tan^{-1} \left(\dfrac{1}{2}\right)$
C $\tan^{-1} \left(\dfrac{1}{4}\right)$
D $\tan^{-1} \left(\dfrac{1}{8}\right)$

Correct answer

C. $\tan^{-1} \left(\dfrac{1}{4}\right)$

Step-by-step solution

Given radius of the park,

r = 10 \text{ m}

Speed of the vehicle,

v = 18 \text{ km/hr} = 18 \times \dfrac{5}{18} \text{ m/s} = 5 \text{ m/s}

The proper angle of banking

\theta

is given by the formula:

\tan \theta = \dfrac{v^2}{rg}

Taking

g = 10 \text{ m/s}^2 and substituting the values:<br><br>

\tan \theta = \dfrac{5^2}{10 \times 10}

<br><br>

\tan \theta = \dfrac{25}{100} = \dfrac{1}{4}

<br><br>

\theta = \tan^{-1}

\left(\dfrac{1}{4}\right)

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