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In the Fig, shown below with what angular speed 'omega' must 'm' with a radius 'r' rotate on a frictionless table so that 'M' does not move ? (b) If m = 1.0 kg, M = 10.0 kg and r = 0.5 m, find omega.

Answer» <html><body><p></p>Solution :(a) Tension in the <a href="https://interviewquestions.tuteehub.com/tag/string-11290" style="font-weight:bold;" target="_blank" title="Click to know more about STRING">STRING</a> = Weight of the hanging mass M.<br/>The tension in the string supplies the required <a href="https://interviewquestions.tuteehub.com/tag/centripetal-415325" style="font-weight:bold;" target="_blank" title="Click to know more about CENTRIPETAL">CENTRIPETAL</a> force to the body of mass m to revolve in a circular orbit of radius r.<br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_NEO_CAO_PHY_XI_V01_MP1_C05_SLV_109_S01.png" width="80%"/><br/>`T=mr <a href="https://interviewquestions.tuteehub.com/tag/omega-585625" style="font-weight:bold;" target="_blank" title="Click to know more about OMEGA">OMEGA</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`<br/>`therefore mr omega^(2)=Mg`<br/><a href="https://interviewquestions.tuteehub.com/tag/angular-11524" style="font-weight:bold;" target="_blank" title="Click to know more about ANGULAR">ANGULAR</a> speed,<br/>`omega = sqrt((Mg)/(mr))=sqrt((10xx9.8)/(1xx0.5))=sqrt(196)=14 rad s^(-1)`.</body></html>


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