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)
V Vakul

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

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