(the image is not exactly acc to the question (longer side is length))
the cylinder of mass mis laid on the moving (towards right with constant acceleration a) trolly . {the cylinder is NOT laid parallel to the side of trolley but it somewhat tilted.} the cylinder makes an angle φ with the line passing through gemotrical ceter and parallel to one of the length of trolley.the cylinder is placed nearer to the back(towards left) edge of trolley . the distance of centre of cylnder from this back edge is d
assume the dimensions of cylinder to be very small in comparison to to other dimensions. neglect slipping .
calculate the distance which the trolly goes befoe the cylinder rolls off the back edge ( answer 3/4 cosec2 φ )
calculate frictional force acting on cylinder
(answer ) 1/3 multiplied √sin2 φ + 9cos2 φ