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A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released in starts performing simple harmonic motion at angular frequency omega. If the radius of the bottle is 2.5 cm then omega is close

Answer» <html><body><p>`2.50 rad"/"s`<br/>`3.75 rad"/"s`<br/>`5.00 rad"/"s`<br/>`1.25 rad"/"s`</p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/according-366619" style="font-weight:bold;" target="_blank" title="Click to know more about ACCORDING">ACCORDING</a> to law of floatation, <br/> (Weight of <a href="https://interviewquestions.tuteehub.com/tag/floating-992903" style="font-weight:bold;" target="_blank" title="Click to know more about FLOATING">FLOATING</a> object)= (Weight of <a href="https://interviewquestions.tuteehub.com/tag/liquid-1075124" style="font-weight:bold;" target="_blank" title="Click to know more about LIQUID">LIQUID</a> displaced by floating object) <br/> `therefore mg = m_(0)g` <br/> `therefore m= m_(0) implies V. p_(0)= Alp_(0)` <br/> `implies l= (m)/(A p_(0))= (m)/(pi R^(2) p_(0))` <br/> `therefore l= (310g)/((3.14)(2.5 cm)^(2)(1-(g)/(cm^3))) approx <a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a> cm approx 0.16 m` <br/> Now angular frequency, <br/> `omega = sqrt((g)/(l)) = sqrt((9.8)/(0.16))= sqrt(61.25)= 7.826 (rad)/(s)` <br/> The nearest value in <a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> options for above answer is `5 rad"/"s`. <br/> `therefore omega approx 5.0 (rad)/(s)`. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P2_C14_E05_066_S01.png" width="80%"/></body></html>


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