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
Answers
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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,
- 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
∴
∴
- This is the angular acceleration. Hence option (D) is correct.
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