A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R , perpendicular to its axis as shown in the figure. The coefficient of friction between the object

Question

A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R , perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is μ . 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?

TestHub · Accepted Answer

F − f = ma f R = I α = I R a ​ ⇒ f = R 2 I a ​ (friction opposes F ). Solid: I = 2 1 ​ m R 2 f = 2 1 ​ ma F = 2 3 ​ ma a = 3 m 2 F ​ Hollow: I = m R 2 f = ma a = 2 m F ​ So a depends on shape: (A) false, (D) true. Rolling without slipping needs f ≤ μ m g ; f is static and equals μ m g only at the limit: (C) false. Solid: f = 2 1 ​ ma ≤ μ m g ⇒ a ma x ​ = 2 μg (B) true.

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Doubts & Discussion

JEE Advanced 2027 (Class 12+)