Question

A person with his hand in his pocket is skating on ice at the rate of \(10 \text{ m s}^{-1}\) and describes a circle of radius \(50 \text{ m}\). What is his inclination to vertical? \((g = 10 \text{ m s}^{-2})\)

• A. \(\tan^{-1}\left(\frac{1}{2}\right)\)
• B. \(\tan^{-1}\left(\frac{1}{5}\right)\)
• C. \(\tan^{-1}\left(\frac{3}{5}\right)\)
• D. \(\tan^{-1}\left(\frac{1}{10}\right)\)

Hint:

For circular motion on ice, inclination depends on centripetal acceleration \(v^2/r\).

Answer 1

The Correct Option is A

Step 1: \[ \tan\theta = \frac{v^2}{rg} \]
Step 2: \[ \tan\theta = \frac{10^2}{50 \times 10} = \frac{100}{500} = \frac{1}{5} \]