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Question: Answered & Verified by Expert
A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20 \mathrm{~m}$. The speed of the car at the top of the hill is between
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Options:
  • A $14 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$
  • B $15 \mathrm{~m} / \mathrm{s}$ and $16 \mathrm{~m} / \mathrm{s}$
  • C $16 \mathrm{~m} / \mathrm{s}$ and $17 \mathrm{~m} / \mathrm{s}$
  • D $13 \mathrm{~m} / \mathrm{s}$ and $14 \mathrm{~m} / \mathrm{s}$
Solution:
2264 Upvotes Verified Answer
The correct answer is: $14 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$

Balancing the forces, we get
$M g-N=M \frac{v^2}{R}$
For weightlessness, $N=0$
$\therefore \frac{M v^2}{R}=M g$
where $R$ is the radius of curvature and $v$ is the speed of car.
Therefore, $v=\sqrt{R g}$
Putting the values, $R=20 \mathrm{~m}, g=10.0 \mathrm{~m} / \mathrm{s}^2$
So, $y=\sqrt{20 \times 10.0}=14.14 \mathrm{~m} / \mathrm{s}^2$
Thus, the speed of the car at the top of the hill is between $14 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$.
Note: The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks.

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