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# A roller coaster is designed such that riders experience " weightlessness" as they go round the top of a hill whose radius of curvature is 20m. The speed of the car at the top of the hill is between

$\begin {array} {1 1} (1)\;13\: m/s\: and \: 14\: m/s & \quad (2)\;14\: m/s\: and \: 15\: m/s \\ (3)\;15\: m/s\: and \: 16\: m/s & \quad (4)\;16\: m/s\: and \: 17\: m/s \end {array}$

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Correct option is (2) At the top of a hill the riders experience weightlessness. It means that the centrifugal force acting on the roller coaster must have a magnitude equal to that of mg , which is it's weight. So balancing these forces we get, v²/R = g Here, R = 20m solving for v, we get v = 14.14 m/s Which lies in between 14m/s and 15m/s