A train is moving with a speed of $12 \mathrm{~m} / \mathrm{s}$ on rails which are $1.5 \mathrm{~m}$ apart. To negotiate a curve radius $400 \mathrm{~m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=$ $10 \mathrm{~m} / \mathrm{s}^2$ ) :
JEE MAIN 2024, Difficult
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$\tan \theta=\frac{\mathrm{v}^2}{\mathrm{Rg}}=\frac{12 \times 12}{10 \times 400}$
$ \tan \theta=\frac{\mathrm{h}}{1.5} $
$ \Rightarrow \frac{\mathrm{h}}{1.5}=\frac{144}{4000} $
$ \mathrm{~h}=5.4 \mathrm{~cm}$
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