A uniform solid cylindrical roller of mass m is being pulled on horizontal surface with force F parallel to the surface applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping, then the value of F is

Question

A uniform solid cylindrical roller of mass m is being pulled on horizontal surface with force F parallel to the surface applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping, then the value of F is, 2 m a, 3 m a, 3 m a 2, 5 m a 2

MARKS App · Accepted Answer

By Newton's law of motion F - f s = m a ...(i) and torque, τ = l α where, α = tangential component of acceleration I = moment of inertia ⇒ f R = l α f R = M R 2 2 · a R ∴ I = M R 2 2 and , α = a R ⇒ f = m a 2 ∴ F = f + m a = m a 2 + m a = 3 m a 2

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