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

Question

A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the types of the car and the road is μs. The maximum safe velocity on this road is : (A) √g R (μs + tan θ/1 - μs tan θ) (B) √(g/R) (μs + tan θ/1 - μs tan θ) (C) √(g/R2) (μs + tan θ/1 - μs tan θ) (D) √g R2 (μs + tan θ/1 - μs tan θ)

Tardigrade Admin · Accepted Answer

(v2/Rg) = ((μs + tan θ/1 - μs tanθ)) ⇒ v = √Rg [(μs + tanθ/1- μs tanθ)]

Q. A car is negotiating a curved road of radius R. The road is banked at an angle $θ$ . The coefficient of friction between the types of the car and the road is $μ_{s}$ . The maximum safe velocity on this road is :

$g R \frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ}$

$\frac{g}{R} \frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ}$

$\frac{g}{R ^{2}} \frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ}$

$g R^{2} \frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ}$

$\frac{v ^{2}}{R g} = (\frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ})$
$\Rightarrow v = R g [\frac{μ _{s} + t a n θ}{1 - μ _{s} t a n θ}]$

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

gR1−μs​tanθμs​+tanθ​​

Rg​1−μs​tanθμs​+tanθ​​

R2g​1−μs​tanθμs​+tanθ​​

gR21−μs​tanθμs​+tanθ​​