Dynamics of uniform and non uniform circular motion

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Question

A train rounds an unbanked circular bend of radius 50 m at a speed of 54 kmh^-1. If g = 10 ms^-2, the angle of banking required to prevent wearing out of rails is given by $θ = \tan^{- 1} (p)$ . The value of $p$ is

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Solution

Now $v = 54 {kmh}^{- 1} = 15 {ms}^{- 1}$ , R = 50 m.
The required angle of banking is given by
$\tan θ = \frac{v^{2}}{Rg} = \frac{15 \times 15}{50 \times 10} = 0 .45$

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