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A cubical block of density rho is floating on the surface of water .Out of its height L, fraction x is submerged in water . The vessel is in an elevator accelerating upward with acceleration a . What is the fraction immersed ?

Answer» <html><body><p></p>Solution :Let density of water is `rho_(w)`. A <a href="https://interviewquestions.tuteehub.com/tag/block-18865" style="font-weight:bold;" target="_blank" title="Click to know more about BLOCK">BLOCK</a> of height L float on it .x be the height of block submerged in water .<br/>Volume of block `V=L^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)`<br/>Mass of block `m=Vrho=L^(3)rhog`<br/><a href="https://interviewquestions.tuteehub.com/tag/weight-1451304" style="font-weight:bold;" target="_blank" title="Click to know more about WEIGHT">WEIGHT</a> of the block `=mg=L^(3)rhog`<br/><img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C10_E04_015_S01.png" width="80%"/><br/>First Case : Volume ofpart of cube submerged in water `=xL^(2)`<br/> `therefore` Weight of water displaced by block `=xL^(2)rho_(w)<a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a>` <br/> Weight of block =weight of water displaced by block .<br/>`L^(3)rhog=xL^(2)rho_(w)g`<br/>`therefore(x)/(L)=(rho)/(rho_(w))`<br/>`thereforex=(rho)/(rho_(w))L`....(1)<br/>Second Case : When vessel is <a href="https://interviewquestions.tuteehub.com/tag/placed-591674" style="font-weight:bold;" target="_blank" title="Click to know more about PLACED">PLACED</a> in an elevator moving upward with acceleration a , then effective acceleration =g=(g+a)<br/>More acceleration a is due to Pseudo force <br/>`therefore` Weight of block =mg<br/>`=m(g+a)`<br/>Suppose , and elevator is moving upward .Let new fraction of block submerged in water is `x_(1)` <br/> For floating of block ,<br/>Weight of block =Weight of displaced water ,<br/>`L^(3)rho(g+a)=x_(1)L^(2)rho_(w)(g+a)`<br/>`therefore(x_(1))/(L)=(rho)/(rho_(w))`....(2)<br/>`x_(1)=(rho)/(rho_(w))*L`<br/>From equation (1)and (2) , <br/> `x=x_(1)`<br/>Hence , the fraction of the block submerged is independent of acceleration.</body></html>


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