Question

The angle of banking ($\theta$) for a meter gauge railway line is given by $\theta = {\sin ^{ - 1}}(\dfrac{1}{{20}})$. What is the elevation of the outer rail in the inner rail?
(A) 4 cm
(B) 5 cm
(C) 8 cm
(D) 12 cm

Answer 1

Hint To answer this question it is required to find the value of $\sin \theta$. This value can be obtained after drawing the figure for the required answer. Once we find the expression for $\sin \theta$, we have to find the value of h that is required.

Complete step by step answer
It should be known to us that for a meter gauge railway which is represented by L = 1 m.
We can also do this as 100 cm.
Given is the figure for better understanding.

From the figure, the value of $\sin \theta = \dfrac{h}{L} = \dfrac{1}{{20}}$.
So, we can write that:
$\dfrac{1}{{20}} = \dfrac{h}{{100}}$
On the evaluation of the above expression we get that:
$20h = 100$
$\Rightarrow h = 5cm$
Therefore, the elevation of the outer rail above the inner rail is 5 cm.

Hence the correct answer is option B.

Note There are various factors on which the angle of banking depends. Here are the reasons listed below:
1. The angle of banking will depend on the speed of the vehicle that is considered, the radius of the curved road also on the acceleration.
2. The expression of the angle of banking does not count on mass. So we can say that the angle of banking does not depend on mass.
3. The angle of banking depends on the radius of the curved road.
4. It should also be remembered that the angle of banking, for a fixed radius will increase with the increase in speed.