A tangential force of 49 N is applied at the highest point of a solid sphere of mass 20 kg resting on a rough horizontal plane. If the sphere rolls without slipping, the acceleration of its centre is:
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A tangential force of 49 N is applied at the highest point of a solid sphere of mass 20 kg resting on a rough horizontal plane. If the sphere rolls without slipping, the acceleration of its centre is:

G1 Physics · Accepted Answer

Let the friction force be f to the right, as required by the rolling condition. Translational equation: F + f = ma. ...(1) Taking clockwise torque about the centre as positive: FR - fR = Iα. For a solid sphere, I = (2/5)mR². For rolling without slipping, α = a/R. Therefore, (F-f)R = (2/5)mR²(a/R) ⇒ F-f = (2/5)ma. ...(2) Add equations (1) and (2): 2F = (7/5)ma. Thus, a = 10F/(7m) = 10×49/(7×20) = 490/140 = 3.5 m/s². Correct option: D.