Question

derive on expression for maximum speed of vehicle along a horizontal circular track ​

Answer 1

Max speed on circular track :

• Let the maximum velocity be v and radius of track be r.

• Now, at limiting conditions, the centripetal force has to be equal to the maximum frictional force of the object.

$F_{c} = f$

$\implies \: \dfrac{m {v}^{2} }{r} = \mu N$

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

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

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

So, max velocity is

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