A solid cylinder of mass m and radius R is kept at rest on a plank of mass 2m lying on a smooth horizontal surface. Massless and inextensible string connecting cylinder to the plank is passing over a

Question

A solid cylinder of mass m and radius R is kept at rest on a plank of mass 2m lying on a smooth horizontal surface. Massless and inextensible string connecting cylinder to the plank is passing over a massless pulley. The friction between the cylinder and the plank is sufficient to prevent slipping. Pulley A is pulled with a constant horizontal force F. Acceleration of plank with respect to earth is

TestHub · Accepted Answer

For the cylinder: 2 F ​ − f = m a c m ​ ...(i) Torque on the cylinder: f R = 2 1 ​ m R 2 α ...(ii) For the plank: 2 F ​ + f = 2 ma ...(iii) Rolling constraint (no slipping): a c m ​ − R α = a ...(iv) On solving (i)-(iv): f = 14 F ​ , a = 7 m 2 F ​ Answer: (D) 7 m 2 F ​

Physics - Rotation Question with Solution | TestHub

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