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QJEEAdv17Ph05b2: JEE Advanced 2017 Physics - Class 11 JEEAdv17Ph05b2 Solution: A wheel of radius R and mass M is placed at the bottom of a…

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

JEE Advanced 2017 Paper 2 Offline Physics - Rotational Motion Question 29 English

Multiple Choice Options

  • A If the force is applied normal to the circumference at point P, then τ is zero
  • B If the force is applied tangentially at point S, then τ ≠ 0 but the wheel never climbs the step
  • C If the force is applied at point P tangentially, then τ decreases continuously as the wheel climbs
  • D If the force is applied normal to the circumference at point X, then τ is constant

Step-by-Step Verified Solution

JEE Advanced 2017 Paper 2 Offline Physics - Rotational Motion Question 29 English Explanation 1
(a) If force is applied normal to surface at P, then line of action of force will pass from Q and thus τ = 0.

(b) Wheel can climb.

(c) τ = F(2Rcosθ) − mgRcosθ

⇒ τ ∝ cosθ

JEE Advanced 2017 Paper 2 Offline Physics - Rotational Motion Question 29 English Explanation 2
Hence, as θ increases, τ decreases. So its correct.

(d) JEE Advanced 2017 Paper 2 Offline Physics - Rotational Motion Question 29 English Explanation 3
τ = Fr⊥ − mgcosθ ; τ increases with θ.

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