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A car is negotiating a curved road of radius R. The road is banked at an angle \theta. The coefficient of friction between the types of the car and the road is \mus. The maximum safe velocity on this road is:

  • Option 1)

    \sqrt{gR^{2}\frac{\mu_{s}+tan\theta}{1-\mu_{2} tan\theta}}

  • Option 2)

    \sqrt {\text{gR}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

  • Option 3)

    \sqrt {\frac{\text{g}} {\text{R}}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

  • Option 4)

    \sqrt {\frac{\text{g}} {{\text{R}^\text{2} }}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

 

Answers (1)

As we learnt in 

If friction is also present in banking of road -

frac{V^{2}}{rg}=frac{mu+tan heta}{1-mu tan heta}

heta= angle of banking

mu= coefficient of friction

V = velocity

- wherein

Maximum speed on a banked frictional road

V=sqrt{frac{rg(mu+tan heta)}{1-mu tan heta}}

 

 V=\sqrt{Rg\frac{\tan \theta +\mu _{s}}{1-\mu _{s}\tan \theta }}


Option 1)

\sqrt{gR^{2}\frac{\mu_{s}+tan\theta}{1-\mu_{2} tan\theta}}

Incorrect

Option 2)

\sqrt {\text{gR}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

Correct

Option 3)

\sqrt {\frac{\text{g}} {\text{R}}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

Incorrect

Option 4)

\sqrt {\frac{\text{g}} {{\text{R}^\text{2} }}\frac{{\mu _\text{s} + \tan \theta }} {{1 - \mu _\text{s} \tan \theta }}}

Incorrect

Posted by

Vakul

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