\textbf{163-} On a curved road, the maximum allowed speed is $54\,\dfrac{\text{km}}{\text{h}}$. If the transverse slope of the road makes an angle of $37°$ with the horizontal, what is the radius of curvature of this curve in meters? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2},\ \sin 37° = 0.6\right.$ and friction on the road surface is negligible.)
$$35 \;(1) \qquad\qquad 40 \;(2) \qquad\qquad 50 \;(3) \qquad\qquad 60 \;(4)$$
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