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A uniformcylinder of length L and mass M having cross - sectional area A is suspended , with its length vertical from a fixed point by a massless spring , such that it is half submerged in a liquidof density sigma atequilibrium position .The extension x_(0)of the spring when it is in equilibrium is .

Answer» <html><body><p>`(<a href="https://interviewquestions.tuteehub.com/tag/mg-1095425" style="font-weight:bold;" target="_blank" title="Click to know more about MG">MG</a>)/k ` <br/>`(Mg)/k (1-(LAsigma)/M)`<br/>`(Mg)/k (1-(LAsigma)/(2M))`<br/>`(Mg)/k (1+(LAsigma)/M)`</p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C06_E05_056_S01.png" width="80%"/><br/> Mass of cross section A , `M = (AL)/2 ` and <a href="https://interviewquestions.tuteehub.com/tag/length-1071524" style="font-weight:bold;" target="_blank" title="Click to know more about LENGTH">LENGTH</a> `L/2 `<br/> ` :. ` Buoyant force in liquid of sensity `sigma `<br/> `F_(B) = igma Mg = sigma (Alg)/2 ` <br/> Suppose extension of spring is `x_(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)`<br/> ` :. ` Restoring force in upward direction in spring ` = kx_(0)`<br/> When k = spring constant and force of <a href="https://interviewquestions.tuteehub.com/tag/weight-1451304" style="font-weight:bold;" target="_blank" title="Click to know more about WEIGHT">WEIGHT</a> on the cylinder in downward direction = Mg <br/> ` :. ` For equilibrium condition of cylinder ,<br/> ` :. mg = (sigmaALg)/2 + kx_(0)` <br/> ` :. kx_(o)=mg - (sigmaALg)/2 ` <br/> ` :. x_(0) =(mg-(sigmaALg)/2)/k` <br/> ` :. x_(0) =(Mg)/k (1- (sigmaLA)/(2M))`</body></html>


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