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Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium ? Give reason for your answer. |
| Answer» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>></p>Solution :`implies` Let the <a href="https://interviewquestions.tuteehub.com/tag/mass-1088425" style="font-weight:bold;" target="_blank" title="Click to know more about MASS">MASS</a> and radius of each identical heavy sphere be M and <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> respectively. An object of mass m be placed at the mid-point P of the line joining their centres. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_029_S01.png" width="80%"/> <br/> Force acting on the object placed at the midpointdue to each sphere `F_1 =F_2 =(<a href="https://interviewquestions.tuteehub.com/tag/gmm-2090431" style="font-weight:bold;" target="_blank" title="Click to know more about GMM">GMM</a>)/((5R)^2)`The direction of forces are opposite, therefore net force acting on the object is zero. This is equilibrium. <br/>If we move object towards A by distance <a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>, <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_029_S02.png" width="80%"/><br/> `F._1=(GMm)/((5R-x)^2)` <br/> `F._2=(GMm)/((5R+x)^2)`<br/> As `F._1 gt F_2,`therefore a resultant force `(F_1 - F_2.)` acts on the object towards sphere A, therefore object start to move towards sphere A and hence equilibrium is unstable.</body></html> | |