A uniform cylinder of diameter 8 cm is kept on a rough inclined plane whose angle of inclination with the ground is 30^(@). What should be the maximum height of the cylinder so that it does not topple?

A uniform cylinder of diameter 8 cm is kept on a rough inclined plane

1.	A uniform cylinder of diameter 8 cm is kept on a rough inclined plane whose angle of inclination with the ground is 30^(@). What should be the maximum height of the cylinder so that it does not topple?
Answer» Solution :The CYLINDER ABCD is kept on the plane of inclination `30^(@)`. Suppose the cylinder is on the verge of toppling over when its HEIGHT is 2 h. At this stage the line of action of gravity MUST pass vertically through the end point A at the base of the cylinder.From Fig tan`30^(@) =(AE)/(EG)` or, `(1)/(sqrt(3))=(r)/(h) " ""or", h = sqrt(3)r = 4sqrt(3) `cm Hence, maximum permissible height = 2h = `2xx4 sqrt(3)` =`8sqrt(3)` cm.