JEE Advanced 2021 Paper 1 Q11 Physics Rotational Mechanics Rolling Motion Hard

JEE Advanced 2021 Paper 1 · Q11 · Rolling Motion

A horizontal force $F$ is applied at the centre of mass of a cylindrical object of mass $m$ and radius $R$, directed horizontally and perpendicular to the cylinder's axis. The cylinder rests on a horizontal surface. The coefficient of friction between the object and the ground is $\mu$. The centre of mass of the object has an acceleration $a$. The acceleration due to gravity is $g$. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?

  1. A. For the same F, the value of a does not depend on whether the cylinder is solid or hollow
  2. B. For a solid cylinder, the maximum possible value of a is 2μg
  3. C. The magnitude of the frictional force on the object due to the ground is always μmg
  4. D. For a thin-walled hollow cylinder, a = F/(2m)
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:B, D

Solution

For pure rolling under horizontal force F at the centre: F − f = ma, fR = Iα, a = Rα. Solving: a = F/(m + I/R²), f = F·(I/R²)/(m + I/R²). Solid cylinder (I = ½mR²): a = 2F/(3m), f = F/3; max F before slipping = 3μmg, giving a_max = 2μg ⇒ (B) correct. Hollow (I = mR²): a = F/(2m), f = F/2 ⇒ (D) correct. (A) wrong since a depends on I (hence on geometry). (C) wrong: friction is static and ≤ μmg, not always equal to μmg.

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