A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.

A rope of negligible mass is wound round a hollow cylinder of mass 3 k

1.	A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope? Assume that there is no slipping.
Answer» Solution :The moment of INERTIA of the hollow cylinder about it axis `I=MR^(2)` [`because` can considered as RING] `3xx(0.4)^(2)` `=0.48kgm^(2)` TORQUE on hollow cylinder `tau=RFsin90^(@)` [`because` Rope is as tangent to cylinder, `theta=90^(@)`] `=RF [because sin90^(@)=1]` `=0.4xx30` `=12NM` Now `tau=Ialphaimpliesalpha=(tau)/(I)` `therefore alpha=(12)/(0.48)=25" RAD s"^(-2)` and tangential ACCELERATION `a_(1)=Ralpha` and radial acceleration `a_(r )=0` `therefore a=sqrt(a_(T)^(2)+a_(r)^(2))` = `sqrt(((Ralpha)^(2)+(0)^(2))^(2))` `=sqrt((0.4xx25)^(2))` `=sqrt((10)^(2))` `therefore a=10ms^(-2)`