Statement I: A cyclist is moving on an unbanked road with a speed of… | JEE Main 2021 (16 Mar, Shift 2)

Q11JEE Main 2021 · 16 MAR · SHIFT 2Medium

Level Road & Rotating Platform

Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh ${}^{-1}$ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s2)

Statement II: If the road is banked at an angle of 45 $^\circ$ , cyclist can cross the curve of 2m radius with the speed of 18.5 kmh ${}^{-1}$ without slipping.

In the light of the above statements, choose the correct answer from the options given below.

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Answer: (b)

Statement I: $v = 7$ km/h $= 1.94$ m/s, $v^2 = 3.78$ ; limit $\mu r g = 0.2 \times 2 \times 9.8 = 3.92$ . Since $3.78 < 3.92$ , no slipping: true.
Statement II: $v_{max}^2 = rg\frac{\mu + \tan\theta}{1 - \mu\tan\theta} = 19.6 \times \frac{1.2}{0.8} = 29.4$ , $v_{max} \approx 5.42$ m/s $\approx 19.5$ km/h.
$18.5$ km/h $< 19.5$ km/h (and above the minimum $\approx 13$ km/h), so no slipping: true.
So the answer is (b) both statements are true.

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