JEE PYQ: Laws Of Motion Question 4
Question 4 - 2021 | 16 Mar Shift 2] (MCQ)
Statement I: A cyclist is moving on an unbanked road with a speed of $7,\text{kmh}^{-1}$ and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve ($g = 9.8,\text{m/s}^2$).
Statement II: If the road is banked at an angle of $45°$, cyclist can cross the curve of 2 m radius with the speed of $18.5,\text{kmh}^{-1}$ without slipping.
(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]
Show Answer
Answer: (4)
Solution
Statement I: $v_{\max} = \sqrt{\mu Rg} = 1.97$ m/s. $7$ km/h $= 1.944$ m/s < $v_{\max}$, safe. Statement II: $v_{\max} = \sqrt{Rg\frac{\tan\theta + \mu}{1-\mu\tan\theta}} = 5.42$ m/s. $18.5$ km/h $= 5.14$ m/s < $v_{\max}$, safe. Both true.
BETA
