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A train has to negotiate a curve of radius 'r' $\mathrm{m}$, the distance between the rails is
${ }^{\prime}{ }^{\prime} \mathrm{m}$ and outer rail is raised above inner rail by distance of ' $\mathrm{h}^{\prime} \mathrm{m}$. If the angle of
banking is small, the safety speed limit on this banked road is
Options:
${ }^{\prime}{ }^{\prime} \mathrm{m}$ and outer rail is raised above inner rail by distance of ' $\mathrm{h}^{\prime} \mathrm{m}$. If the angle of
banking is small, the safety speed limit on this banked road is
Solution:
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Verified Answer
The correct answer is:
$\sqrt{\operatorname{rg}\left(\frac{h}{\ell}\right)}$
$\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\mu \mathrm{R}=\mu \mathrm{mg}$
$\mathrm{v}^{2}=\mu \mathrm{gr}$
$\mathrm{v}=\sqrt{\mu \mathrm{gr}}=\sqrt{\tan \theta \mathrm{gr}}=\sqrt{\sin \theta \mathrm{g} \mathrm{r}}$$[$ For small angle of $\theta]$
$=\sqrt{\mathrm{gr} \frac{\mathrm{h}}{\ell}}$
$\mathrm{v}^{2}=\mu \mathrm{gr}$
$\mathrm{v}=\sqrt{\mu \mathrm{gr}}=\sqrt{\tan \theta \mathrm{gr}}=\sqrt{\sin \theta \mathrm{g} \mathrm{r}}$$[$ For small angle of $\theta]$
$=\sqrt{\mathrm{gr} \frac{\mathrm{h}}{\ell}}$
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