1.

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_DOC_OBJ_PHY_XI_V01_B_C07_SLV_031_S01.png" width="80%"/><br/>(a) The Cylinder will slide if<br/>`Mg <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a> theta gt mu Mg cos theta rArr tan theta 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 topple if<br/>`(Mg sin theta) (h)/(2)gt (M <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> cos theta) r rArr tan theta gt (2r)/(h)` ...(2)<br/>Thus, the condition of sliding is `tan theta gt mu` and condition of toppling `tan theta 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/>(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>) The cylinder will topple before sliding if `mu gt (2r)/(h)`</body></html>


Discussion

No Comment Found

Related InterviewSolutions