#### Question

A vehicle is moving on a circular track whose surface is inclined towards the horizon at an angle of 10°. The maximum velocity with which it can move safely is 36 km / hr. Calculate the length of the circular track. [π = 3.142]

#### Solution

Given, angle of banking, θ = 10°

Optimum speed, V_{0} = 36 km/hr = 36 x `5/18` m/s.

Or, V_{0 }= 10 m/s

Let R be the radius of the circular track

We have,

V_{0 }= `sqrt( gRtanθ )`

⇒ `V_0^2` = gRtanθ

⇒ R = `V_0^2/[ g tanθ ]`

= `(10m/s)^2/[(9.8m/s^2) xx tan 10^0]`

= `[100m]/[ 9.8 xx 0.1763 ]`

⇒ R = 57.88 m

∴ Length of the circular track = 2πR = 2 x 3.142 x 57.88 = 363.72m.

Is there an error in this question or solution?

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A Vehicle is Moving on a Circular Track Whose Surface is Inclined Towards the Horizon at An Angle of 10°. the Maximum Velocity with Which It Can Move Safely is 36 Km / Hr. Calculate The Length Concept: Uniform Circular Motion.

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