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? Answer this question..with proper explaination...Thanks!
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Asked by vidyavikram10 | 12 Mar, 2020, 11:21: AM
answered-by-expert Expert Answer
Buoyancy force F acting on block of mass m is given by, F= V × ( ρS - ρl ) g
 
where V is volume , ρS is density of solid, ρl is density of liquid and g is acceleration due to gravity
 
F = V × [  (5/2)do - 4do + ( 3y do /ho ) ] g  = - (3V do g) /ho [ (ho/2) - y ]
 
Hence if we take the height ( ho/2 ) as equilibrium position,
we find force is proportional to displacement with respect to equlibrium position.
 
Sign of the force -ve shows it is restoring force. Hence the motion is SHM
 
Force constant k = (3V do g) /ho
 
angule frequency ω of SHM  is given by ,  begin mathsize 14px style omega space equals space square root of k over m end root space space equals space square root of fraction numerator 3 space V space g space d subscript o over denominator m space h subscript o end fraction end root space end style
since density of solid block is (5/2)do , we get ( V do / m ) = 2/5
 
Hence begin mathsize 14px style omega space equals space square root of fraction numerator 1.2 space g over denominator h subscript o end fraction end root end style
Time period T  is given by, begin mathsize 14px style T space equals space fraction numerator 2 pi over denominator omega end fraction space equals 2 pi square root of fraction numerator 1.2 space h subscript o over denominator g end fraction end root space end style
Answered by Thiyagarajan K | 12 Mar, 2020, 15:14: PM

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