# Q5.31 A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 106 kg. What provides the centripetal force required for this purpose — The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

The required centripetal force is provided by the rails, as by Newton's third law of motion, wheels apply force on the rails and thus rails provides a force on the wheels (action-reaction pair).

We know that the angle of banking is given by :

$\tan \Theta \ =\ \frac{v^2}{rg}$

or                                                                $=\ \frac{15^2}{30\times10}$

or                                                                $=\ 0.75$

Thus                                                    $\Theta \ =\ 36.87^{\circ}$

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