Question 4 : A uniform cylinder of mass 'M' and radius 'R' is to be pulled over a step of height 'a' (a<R) by a force 'F'at it's centre 'O' perpendicular to the plane through the axis of the cylinder on the edge of the step as shown in figure. The minimum value of 'F' required is Answer: Apply the principle of moment about the edge of the step C Sum of clockwise moment=Sum of anticlockwise moment Just before rolling `F× R=Mg×d`---------------(1) (where d=CB from figure) Applying Pythagores theorem in đťš«OBC `R^2=(R-a)^2+d^2` `d=sqrt(R^2-(R-a)^2)` substitute for d in (1) `F=(Mg/R)×R×sqrt(1-((R-a)/R)^2)` `F=Mg×sqrt(1-((R-a)/R)^2)` Watch Video with explanation