A L shaped container has dimensions shown in the fig. It has circular cross section of radius R. It is placed on a smooth horizontal table. The container is divided into two equal sections by a membrane AB. One section contains nitrogen and the other one contains oxygen. Temperature of both sides is same but pressure in the compartment having `N_(2)` is 4 times that in the other compartment. Due to some reason the membrane gets punctured. Find the distance moved by the cylinder if the cylinder is constrained to move in x direction only [with the help of guiding walls `W_(1) " and " W_(2)`]. There is no friction anywhere and mass of the cylinder and membrane is negligible

Answer

0.83 R towards left