Question

On a railway curve, the outside rail is laid higher than the inside one so that the resultant force exerted on the wheels of the rail car by the tops of the rail will:
A. Have a horizontal inward component
B. Be vertical
C. Equilibrate the centripetal force
D. Be decreased

Answer 1

Hint:Try to balance various forces with each other, horizontal forces will be balanced by opposite horizontal forces and vertical forces will be balanced by vertical force in opposite direction. Firstly find out various forces acting on the body and then try to balance them.

Formula section:
 \[N\cos \theta \]= vertical component of normal reaction has an angle of \[\theta \]
 \[N\sin \theta \]=horizontal component of normal reaction has an angle of \[\theta \]
$m{{w}^{2}}r$= centripetal force
m = mass
w = angular velocity
r = radius

Complete step by step solution:
In this question we will take a normal reaction on the wheels (normal reaction is a contact force and it acts only on those bodies which are in contact with the surface, so here wheels are in contact with ground so normal reaction acts only on the wheels) this normal reaction will have two components.

The vertical component equates with weight and the horizontal component is equated by centripetal force (this centripetal force helps in circular motion). Suppose normal reaction has an angle of \[\theta \] with the vertical, so its vertical component will be \[N\cos \theta \] and horizontal component will be \[N\sin \theta \] (\[\left( N \right)\] represents normal reaction on the wheels).
\[N\cos \theta =mg\]
\[N\sin \theta =m{{w}^{2}}r\]
It represents centripetal force which is always directed towards the centre here it means towards the inward side. Therefore, it is proved that force exerted on the wheels has an inward horizontal component.

Hence option A is correct.

Note: Kindly note that here normal reaction on wheels is at a certain angle with vertical so, it will automatically have two components.The force surfaces apply to stop solid objects from passing through one another is known as the normal force. A contact force is a normal force. A normal force cannot be applied between two surfaces that are not in contact.