question_answer

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            [AIPMPT (S) 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

Correct Answer: A

Solution :

Balancing the forces, we get

\[Mg-N=M\frac{{{v}^{2}}}{R}\]

For weightlessness, \[N=0\]

\[\therefore \]      \[\frac{M{{v}^{2}}}{R}=Mg\]

where R is the radius of curvature and v is the speed of car.

Therefore, \[v=\sqrt{Rg}\]

Putting the values, \[R=20\text{ }m,\,\,g=10.0\text{ }m/{{s}^{2}}\]

So,       \[v=\sqrt{20\times 10.0}=14.14\,m\text{/}{{s}^{2}}\]

Thus, the speed of the car at the top of the hill is between 14 m/s and 15 m/s.

Note:    The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks.