Question

what is the maximum speed limit of vehicle when it moves on a rough horizontal circular path​

Answer 1

Given:

Vehicle of moving on a rough horizantal circular road.

To find:

Maximum speed limit ?

Calculation:

Let the max speed for the vehicle be v.

At critical conditions, the speed should be such that the centripetal force will be equal and opposite to the frictional force.

$\rm \therefore \: \dfrac{m {v}^{2} }{r} = f$

$\rm \implies\: \dfrac{m {v}^{2} }{r} = \mu(normal \: reaction)$

$\rm \implies\: \dfrac{m {v}^{2} }{r} = \mu(mg)$

$\rm \implies\: \dfrac{{v}^{2} }{r} = \mu g$

$\rm \implies\: {v}^{2} = \mu rg$

$\rm \implies\:v = \sqrt{\mu rg}$

So, the max speed limit will be :

$\boxed{ \bold{\:v = \sqrt{\mu rg}}}$