Question

A vehicle is moving on a circular track whose surface is inclined towards the horizon at an angle of ${10}^o$. The maximum velocity with which it can move safely is $36km/hr$. Calculate the length of the circular track. $[\pi =3.142]$.

Answer 1

Vehicle is moving on a circular track whose surface is inclined towards the horizon at an angle $\theta =10$.
The forces acting in horizontal direction and vertical direction are centripetal force and the weight of vehicle respectively.
If v be the velocity of car where v=36km/hr=10m/s and r be the radius of track .
Centripetal force $F_c=m\frac{v^2}{r}$
and weight W=mg .
Resolving the forces along the incline .
$mg\sin \theta =m\frac{v^2}{r}\cos \theta$
$r=\frac{v^2\cot \theta }{g}$
r=56.7 m
Lenght of circular track= $2\pi r=356m$