A cylinder, on a level surface angularly accelerates as a string wrapped around is put under tension. Because this string causes the cylinder to roll without slipping, the tension force cannot to any work because it is applied to a point on the surface for a zero distance. How then, can the rotational kinetic energy increase if there are no sources of work.
closed as off-topic by Aaron Stevens, Carl Brannen, GiorgioP, Jon Custer, Yashas Apr 24 at 15:44
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In your question I think that you are asking that the point of application of tension doesn't slips on ground so work done by tension is zero(but it is not zero!) then why rotational K.E is increasing?
Take a look at the situation for a moment carefully then read the next paragraph.
See the tension produces a torque around the axis passing through cylinder's centre.The torque does work which can be calculated by the integral of dot product of torque and infinitesimal angular displacement.
By work energy theorem if torque does work then it must lead to change in kinetic energy of the cylinder.Hope this helps!