A small roller coaster starts at point $A$ with a speed $u$ on a curved track as shown in the figure.
The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point $D$ on the track will be:

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${(u^{2} + g h)}^{1 / 2}$

${(u^{2} + 2 g h)}^{1 / 2}$

${(u^{2} + 4 g h)}^{1 / 2}$

$u$

answer is C.

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Detailed Solution

Let the speed of the roller coaster at point $D$ be $v$ .

Applying the law of conservation of energy between points $A$ and $D$ , we get:

$\frac{1}{2} m u^{2} + m g (2 h) = \frac{1}{2} m v^{2} + 0 \Rightarrow u^{2} + 4 g h = v^{2} \Rightarrow v = \sqrt{u^{2} + 4 g h}$

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