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

• A

  $13 \mathrm{~m} / \mathrm{s}$ and $14 \mathrm{~m} / \mathrm{s}$
• Correct answer
  B

  $14 \mathrm{~m} / \mathrm{s}$ and $15 \mathrm{~m} / \mathrm{s}$
• C

  $15 \mathrm{~ms} /$ and $16 \mathrm{~m} / \mathrm{s}$
• D

  $16 \mathrm{~m} / \mathrm{s}$ and $17 \mathrm{~m} / \mathrm{s}$

Solution

Actually, $m g-N=\frac{m v^2}{r}$ For weightlessness, $\quad N=0$ $$ \begin{aligned} \therefore m g & =\frac{m v^2}{r} \\ v & =\sqrt{g r} \\ & =\sqrt{10 \times 20} \mathrm{~ms}^{-1}=14.14 \mathrm{~ms}^{-1} \end{aligned} $$

Hence, the correct answer is option: 'B'.