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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]
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Solution
Given, angle of banking, θ = 10°
Optimum speed, V0 = 36 km/hr = 36 x `5/18` m/s.
Or, V0 = 10 m/s
Let R be the radius of the circular track
We have,
V0 = `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.
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