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A uniform cylinder of height h and radius r is placed with its circular face on a rough inclined plane and the inclination of the plane to the horizontal gradually in creased. If mu is the coefficeint of friction, then under what conditions the cylinder will a) slide before topping b) topple before sliding

Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_NEO_CAO_PHY_XI_V01_B_C07_SLV_091_S01.png" width="80%"/> <br/> (a) The Cylinder will slide if <br/> `Mgsintheta gt mu Mgcosthetaimpliestantheta gt mu`……….`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)` <br/> The cylinder will <a href="https://interviewquestions.tuteehub.com/tag/topple-3224023" style="font-weight:bold;" target="_blank" title="Click to know more about TOPPLE">TOPPLE</a> if <br/> `(Mgsintheta)(h)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) gt (Mg costheta)rimpliestantheta gt (2r)/(h)`…………`(2)` <br/> <a href="https://interviewquestions.tuteehub.com/tag/thus-2307358" style="font-weight:bold;" target="_blank" title="Click to know more about THUS">THUS</a>, the condition of sliding is `tantheta gt mu` and condition of toppling `tantheta gt (2r)/(h)`. Hence, the cylinder will slide before toppling if `mu <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> (2r)/(h)` <br/> (b) The cylinder will topple before sliding if `my gt (2r)/(h)`</body></html>


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