A homogeneous solid cylinder of length L (L

Question

(A) For the cylinder to float in equilibrium, the weight of the cylinder must be equal to the total upthrust (buoyant force) exerted by the two liquid

Vedclass · Accepted Answer

$\frac{5}{4} d$

Vedclass · Answer

(A) For the cylinder to float in equilibrium, the weight of the cylinder must be equal to the total upthrust (buoyant force) exerted by the two liquids.Let $A'$ be the cross-sectional area of the cylinder. The volume of the cylinder is $V = A' L$.Weight of the cylinder $W = V D g = A' L D g$.The upthrust from the lighter liquid (density $d$) is $F_1 = (	ext{Volume in lighter liquid}) 	imes d 	imes g = (A' 	imes \frac{3L}{4}) d g$.The upthrust from the denser liquid (density $2d$) is $F_2 = (	ext{Volume in denser liquid}) 	imes 2d 	imes g = (A' 	imes \frac{L}{4}) 	imes 2d 	imes g$.Equating weight to total upthrust:$A' L D g = (A' 	imes \frac{3L}{4}) d g + (A' 	imes \frac{L}{4}) 	imes 2d 	imes g$Dividing both sides by $A' L g$:$D = \frac{3}{4} d + \frac{2}{4} d$$D = \frac{5}{4} d$

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