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CBSE Class 11-science Answered

A small spherical object having density 2P is placed inside the liquid of density P and connected to an ideal string of length l whose other end is kept fixed so that the object can move in a vertical cirlcle, minimum speed which must be given at the bottom to just complete the vertical circle.
Asked by dhruvund8769 | 04 Feb, 2023, 11:41: PM
answered-by-expert Expert Answer
Force F acting on sphere when it is inside liquid , F = begin mathsize 14px style V space left parenthesis space rho subscript s minus rho subscript l right parenthesis space g end style
where V is volume of sphere, begin mathsize 14px style rho subscript s end style is density of sphere , begin mathsize 14px style rho subscript l end style is density of liquid and g is acceleration due to gravity.
 
Potential energy diference ΔU between point A and point B is
 
begin mathsize 14px style capital delta U space equals left square bracket space V space left parenthesis rho subscript s minus space rho subscript l right parenthesis space g space right square bracket space left parenthesis 2 l space right parenthesis end style
Above potential energy difference equals to the minimum energy Emin required to move the sphere from point A to point B in circular path.
 
if begin mathsize 14px style rho subscript s end style= 2P  and begin mathsize 14px style rho subscript l end style = P , then minimum energy Emin required to make the sphere to move in full circle is
 
Emin = [ V × P × g ] ( 2 l )
Answered by Thiyagarajan K | 05 Feb, 2023, 02:41: PM

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