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4-1.Newton's Laws of Motion
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A cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$ through which the cyclist leans inwards is given by
A$\tan \theta = \frac{{Rg}}{{{v^2}}}$
B$\tan \theta = {v^2}Rg$
C$\tan \theta = \frac{{{v^2}g}}{R}$
D$\tan \theta = \frac{{{v^2}}}{{Rg}}$
Solution
For a banked road or cyclist
${\mathrm{N} \cos \theta=\mathrm{mg}}$
${\mathrm{N} \sin \theta=\frac{\mathrm{mv}^{2}}{\mathrm{R}}}$
$\mathbf{o r}$ ${\tan \theta=\frac{\mathrm{v}^{2}}{\mathrm{Rg}}}$
${\mathrm{N} \cos \theta=\mathrm{mg}}$
${\mathrm{N} \sin \theta=\frac{\mathrm{mv}^{2}}{\mathrm{R}}}$
$\mathbf{o r}$ ${\tan \theta=\frac{\mathrm{v}^{2}}{\mathrm{Rg}}}$
Standard 11
Physics
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