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Rotational Dynamics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsRotational Dynamics3 Marks
Question
A vehicle is moving on a circular track whose surface is inclined towards the horizontal at an angle of \(10^{\circ}\). The maximum velocity with which it can move safely is \(36 km / hr\). Calculate the length of the circular track.
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Answer

Given, angle of banking, $\theta=10^{\circ}$
Optimum speed, $V_0=36 km / hr =36 \times \frac{5}{18} m / s$
Or, $V_0=10 m / s$
Let $R$ be the radius of the circular track
We have,
$V_0=\sqrt{g R \tan \theta}$
$\Rightarrow V_0^2=g R \tan \theta$
$\Rightarrow R=\frac{V_0^2}{g \tan \theta}$
$=\frac{\left(10 \frac{m}{3}\right)^2}{\left(9.8 \frac{m}{3}\right) \times \tan 10^0}$
$=\frac{100 m}{9.8 \times 0.1763}$
$\Rightarrow R=57.88 m$
$\therefore \text { Length of the circular track }=2 \pi R=2 \times 3.142 \times 57.88=363.72 m .$

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