MHT CET · Physics · Laws of Motion
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
- A \(\sqrt{\operatorname{rg}\left(\frac{h}{\ell}\right)}\)
- B \(\operatorname{rg} \frac{h}{\ell}\)
- C \(\frac{\left(\frac{h}{\ell}\right)^{2}}{r g}\)
- D \(\left(\operatorname{rg} \frac{h}{\ell}\right)^{2}\)
Answer & Solution
Correct Answer
(A) \(\sqrt{\operatorname{rg}\left(\frac{h}{\ell}\right)}\)
Step-by-step Solution
Detailed explanation
\(\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\mu \mathrm{R}=\mu \mathrm{mg}\)
\(\mathrm{v}^{2}=\mu \mathrm{gr}\)
\(\mathrm{v}=\sqrt{\mu \mathrm{gr}}=\sqrt{\tan \theta \mathrm{gr}}=\sqrt{\sin \theta \mathrm{g} \mathrm{r}}[\) 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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