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

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, \[v=\sqrt{20\times 10.0}=14.14\,m/{{s}^{2}}\] Thus, the speed of the car at the top of the hill is between 14 m/s and 15 m/s.