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Statement I: A cyclist moving at 7 km/h on an unbanked road takes a sharp circular turn of radius 2 m without slowing down. With a coefficient of static friction 0.2 (g = 9.8 m/s²), the cyclist will not skid and will negotiate the curve. Statement II: If the road is banked at 45 deg, the cyclist can take a curve of radius 2 m at a speed of 18.5 km/h without slipping. Choose the correct option.

1. Statement I is incorrect and Statement II is correct.
2. Statement I is correct and Statement II is incorrect.
3. Both Statement I and Statement II are false.
4. Both Statement I and Statement II are true.

Correct answer: Both Statement I and Statement II are true.

Solution

Statement I: v = 7 km/h ~= 1.94 m/s, v² = 3.78; mu*g*r = 0.2*9.8*2 = 3.92 > 3.78, so the cyclist passes -> true. Statement II: with theta=45 deg and mu=0.2, v_max² = g*r*(1+mu)/(1-mu) = 9.8*2*1.2/0.8 = 29.4, v_max ~= 5.42 m/s ~= 19.5 km/h > 18.5 km/h, so true.

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