Question

A car of mass m is moving on a level circular track of
radius R. If μ represents the static friction between
the road and tyres of the car, the maximum speed of
the car in circular motion is given by ?​

Answer 1

Need to FinD :-

• The maximum speed of the car in the circular motion .

$\red{\frak{Given}}\begin{cases} \textsf{ A car of mass m is moving on a level circular track of</p><p>radius R.} \\\\\sf \mu \ \textsf{ represents the static friction between the road and tyres of the car. }\end{cases}$

Given that , the car of mass m , is moving on a circular track of radius R . We know that , the centripetal force provides the force for the motion . The centripetal force is given by ,

$\longrightarrow\small \sf \red{ Force_{(Centripetal)}= \dfrac{ mass * ( velocity)^2}{Radius }}$

Also , the centripetal force here is provided by the frictional force. The frictional force is given by ,

$\longrightarrow\small \sf Force_{(Friction)}= \mu * Normal \ force$

And N = mg , therefore ,

$\longrightarrow\small \sf \red{ Force_{(Friction)}= \mu \ mg}$

Therefore ,

$\longrightarrow\small \sf Force_{(Friction)}= Force_{( Centripetal)} \\\\\\\sf\longrightarrow \small \mu mg = mv^2/r \\\\\\\sf\longrightarrow \small v^2 = \dfrac{ \mu mg R }{m } \\\\\\\sf\longrightarrow \small v^2 = \mu g R \\\\\\\sf\longrightarrow \small \underline{\underline{\red{\sf Velocity_{(max)}= \sqrt{ \mu R g} }}}$

$\rule{200}2$