# A Train Has To Negotiate A Curve Of Radius 400 M. By How Much Should The Outer Rail Be Raised With Respect To Inner Rail For A Speed Of 48 Km/Hr. The Distance Between The Rail Is 1 M.

Sol:

The radius of the curved path is r.

The width of the path is b

The value of h is given by

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

Now, by substituting the values given in the question:

$$v = 48Km/h = \frac{40}{3}m/s$$ $$b = 1m, r = 400m and g = 9.8m/s^{2}$$ $$\Rightarrow h = \frac{\frac{40^{2}}{3} * 1}{400 * 9.8}$$ $$\Rightarrow h = 0.0045 m or 4.54 cm$$

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