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» <html><body><p></p>Solution :The <a href="https://interviewquestions.tuteehub.com/tag/cylinder-942617" style="font-weight:bold;" target="_blank" title="Click to know more about CYLINDER">CYLINDER</a> ABCD is kept on the plane of inclination `30^(@)`. Suppose the cylinder is on the verge of toppling over when its <a href="https://interviewquestions.tuteehub.com/tag/height-1017806" style="font-weight:bold;" target="_blank" title="Click to know more about HEIGHT">HEIGHT</a> is 2 h. At this stage the line of action of gravity <a href="https://interviewquestions.tuteehub.com/tag/must-2185568" style="font-weight:bold;" target="_blank" title="Click to know more about MUST">MUST</a> pass vertically through the end point A at the base of the cylinder.From Fig <br/> tan`30^(@) =(AE)/(EG)` <br/> or, `(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(sqrt(3))=(r)/(h) " ""or", h = sqrt(3)r = 4sqrt(3) `cm <br/> Hence, maximum permissible height = 2h = `2xx4 sqrt(3)` <br/> =`8sqrt(3)` cm. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CHY_DMB_PHY_XI_P1_U05_C01_SLV_027_S01.png" width="80%"/></body></html>