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Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Laws of Motion
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A cyclist has to lean inwards when negotiating a curved unbanked road. The cyclist leans with an angle $\theta$ to the vertical. $N$ is the normal reaction given by $N=mg$, where $m$ is the mass of the cyclist and the bicycle combined. The radius of the curved road is $R$. The force of friction is given by $F=\mu N$ where $\mu$ is the co-efficient of friction. Assuming the cyclist skids which of the following is true?

$v \gt \sqrt {\mu g R}, \quad v \lt \sqrt {\mu g R},\quad$$v = \sqrt {\mu m g R},$$\quad v \gt \sqrt {\mu m g R}$
Can you answer this question?
 
 

1 Answer

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The problem can be represented as follows:
$F = \mu N = \mu m g$.
The cyclist will skid if the centripetal force $\large\frac{mv^2}{R}$ exceeds the frictional force $F = \mu m g$.
$\Rightarrow$ the cyclist skids if $v \gt \sqrt{\mu g R}$
answered Aug 25, 2014 by balaji.thirumalai
 

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