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Q.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\pi = 3.142]

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2017Subjective· 3mImportance★★★★★
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For a vehicle safely negotiating a banked (frictionless) circular track, tan⁡θ=vmax2rg\tan\theta = \dfrac{v_{max}^2}{rg}.

For a vehicle moving on a circular track banked at angle θ\theta, the maximum safe speed (with friction neglected, i.e. banking alone providing the necessary centripetal force) satisfies

tan⁡θ=vmax2rg\tan\theta = \frac{v_{max}^2}{rg}

Given: θ=10∘\theta = 10^{\circ}, vmax=36 km/h=10 m/sv_{max} = 36\ \text{km/h} = 10\ \text{m/s}, g=9.8 m/s2g = 9.8\ \text{m/s}^2.

r=vmax2gtan⁡θ=(10)29.8×tan⁡10∘r = \frac{v_{max}^2}{g\tan\theta} = \frac{(10)^2}{9.8\times\tan10^{\circ}}

With tan⁡10∘≈0.1763\tan10^{\circ}\approx 0.1763:

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