Gravitation Ques 13
13. A roller coaster is designed such that riders experience “weightlessness” as they go round the top of a hill whose radius of curvature is $20$ $ m$. The speed of the car at the top of the hill is between:
[2008]
(a) $14$ $ m / s$ and $15$ $ m / s$
(b) $15$ $ m / s$ and $16$ $ m / s$
(c) $16$ $ m / s$ and $17$ $ m / s$
(d) $13$ $ m / s$ and $14$ $ m / s$
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Answer:
Correct Answer: 13.(a)
Solution:
- (a) For the riders to experience weightlessness at the top of the hill, the weight of the rider must be balanced by the centripetal force.
i.e., $m g=\frac{m v^{2}}{R}$
$\Rightarrow \quad v=\sqrt{g R}=\sqrt{10 \times 20}=14.1 $ $ms^{-1}$
Hence, the speed of the car should be between $14 $ $ms^{-1}$ and $15$ $ ms^{-1}$.
BETA
