Question

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:
(A) 3F/2mR
(B) F/3mR
(C) F/2mR
(D) 2F/3mR

Answer 1

The angular acceleration of the cylinder will be 2F/3mR .

Solution :

• Refer the diagram attached.
• At any instant, the cylinder will rotate about an axis O which is on the surface of the cricket pitch.
• The force F is applied at the center of mass of the cylinder.
• Let I₀ be the moment of inertia of the cylinder about the axis O.
• Moment of inertia of a solid cylinder about its axis is given by,

        $I = \frac{1}{2}MR^{2}$

• Hence, by parallel axis theorem , the moment of inertia of the cylinder about the axis O will be,

        I₀ = 1/2(MR²) + MR²

        I₀ = 3/2(MR²)

• Let α be the angular acceleration.

     ∴  F×R = I₀α

     ∴ $F.R = \frac{3}{2} MR^{2} \alpha$  

     ∴  $\alpha = \frac{2F}{3MR}$  

• This is the angular acceleration. Hence option (D) is correct.