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 15m/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 m, g =10.0 m/s2 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.