Question
A car is taking turn on the rough banked circular track. What should be the velocity of car so that there is no wear and tear of the tyres?
Solution
Consider a car of mass m taking the turn on banked rough circular track of radius r.
Let 
be the angle of banking and μ be the coefficient of friction.
Let u be the velocity of car so that there is no wear and tear.
Different forces acting on car are:
(i) Weight of car, acting vertically downwards.
(ii) Reaction R on car, normal to track.
(iii) Frictional force f = μR, down the inclined plane.
(iv) Centrifugal force ![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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, radially outwards.
Resolving the rectangular component of different forces.
Since there is no wear and tear on the car, therefore, net force in vertical and horizontal direction is zero.
That is, 
