Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A roller coaster is designed such that riders experience "weightlessness" as they go around the top of a hill whose radius of curvature is $20 \text{ m}$ . The speed of the car at the top of the hill is between:

$14 \text{ m/s}$ and $15 \text{ m/s}$

$15 \text{ m/s}$ and $16 \text{ m/s}$

$16 \text{ m/s}$ and $17 \text{ m/s}$

$13 \text{ m/s}$ and $14 \text{ m/s}$

Step-by-Step Solution

Condition for Weightlessness: Riders experience weightlessness at the top of the hill when the normal reaction force ( $N$ ) exerted by the seat on them becomes zero. In this condition, the gravitational force alone provides the necessary centripetal force required for circular motion.
Equation of Motion: At the top of the vertical path: $mg - N = \frac{mv^2}{R}$ Setting $N = 0$ for weightlessness: $mg = \frac{mv^2}{R}$ $v = \sqrt{Rg}$
Calculation: Given $R = 20 \text{ m}$ and approximating $g \approx 9.8 \text{ m/s}^2$ to $10 \text{ m/s}^2$ : $v = \sqrt{20 \times 10} = \sqrt{200} \approx 14.14 \text{ m/s}$ Using $g = 9.8 \text{ m/s}^2$ : $v = \sqrt{20 \times 9.8} = \sqrt{196} = 14 \text{ m/s}$
Conclusion: The speed is approximately $14.14 \text{ m/s}$ , which falls between $14 \text{ m/s}$ and $15 \text{ m/s}$ . (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Section 5.10 Circular Motion).

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