Question

A rail road curve is to be laid out on a circle. The radius to be used if the track is to change direction by ${30}^{\circ }$ in a distance of $60m=$

• A. $\frac{90}{\pi }m$
• B. $\frac{360}{\pi }m$
• C. $\frac{240}{\pi }m$

Answer 1

The correct option is B $\frac{360}{\pi }m$

Here, the rail road has to change direction by ${60}^{\circ }$ while travelling a distance of $60m.$
The situation can be represented as:

Now, using the formula for length of an arc:
$l=\frac{\alpha }{{360}^{\circ }}\times 2\pi \times r$

$60=\frac{{30}^{\circ }}{{360}^{\circ }}\times 2\pi \times r$​​​​​​​

$\Rightarrow 60=\frac{1}{12}\times 2\pi \times r$​​​​​​​

$\Rightarrow r=\frac{360}{\pi }m$