Question

A train has to negotiate a curve of radius \( r \) m, the distance between the rails is \( \ell \) m and outer rail is raised above inner rail by distance of \( h \) m. If the angle of banking is small, the safety speed limit on this banked road is

• A. \( \sqrt{rg \frac{h}{\ell}} \)
• B. \( \frac{h}{rg} \frac{\ell}{r} \)
• C. \( \frac{h}{r\ell} \)
• D. \( (rg \frac{h}{\ell})^2 \)

Hint:

For a banked curve, the safety speed depends on the radius of the curve, the height difference, and the distance between the rails.

Answer 1

The Correct Option is A

Step 1: Safety speed equation.
The safety speed limit for a train negotiating a curve is determined by the formula: \[ v = \sqrt{r g \frac{h}{\ell}} \] Where \( r \) is the radius of curvature, \( g \) is the acceleration due to gravity, \( h \) is the height difference between the rails, and \( \ell \) is the distance between the rails. Thus, the correct answer is (A) \( \sqrt{rg \frac{h}{\ell}} \).