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One end of a U-tube containing mercury is connected to a suction pump and the other end to atmosphere. A small pressure difference is maintained between the two columns. Show that, when the suction pump is removed, the column of mercury in the U-tube executes simple harmonic motion.

Answer» <html><body><p></p>Solution :When suction pump connected through one end of U-tube, the mercury depressed by h in one limb and in other arm mercury raised by 2h. <br/> The difference in height of mercury in both the limbs = <a href="https://interviewquestions.tuteehub.com/tag/2y-301307" style="font-weight:bold;" target="_blank" title="Click to know more about 2Y">2Y</a> and pressure of `P = 2hpg` in this arms. Here p= density of mercury and g is the acceleration <a href="https://interviewquestions.tuteehub.com/tag/due-433472" style="font-weight:bold;" target="_blank" title="Click to know more about DUE">DUE</a> to <a href="https://interviewquestions.tuteehub.com/tag/gravity-18707" style="font-weight:bold;" target="_blank" title="Click to know more about GRAVITY">GRAVITY</a>. If the cross sectional area of arms is A, then force produced due to height of 2h, <br/> `<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>= PA` <br/> `=2hpg xxA = (<a href="https://interviewquestions.tuteehub.com/tag/2pga-1836135" style="font-weight:bold;" target="_blank" title="Click to know more about 2PGA">2PGA</a>)h` <br/> `therefore F propto h ""therefore F = kh` <br/> Where `k= 2pgA` is constant. <br/> This force is opposite to displacement, `F= -kh` <br/> Hence, restoring force acts on oscillation of mercury column is directly proportional to displacement and opposite to displacement. So the motion of mercury in U-tube is simple harmonic motion.</body></html>


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