A homogeneous solid cylinder of length L (L

Question

(A) For the cylinder to float in equilibrium,its weight must be equal to the total upthrust (buoyant force) exerted by the two liquids.Weight of the c

Vedclass · Accepted Answer

$\frac{5}{4}d$

Vedclass · Answer

(A) For the cylinder to float in equilibrium,its weight must be equal to the total upthrust (buoyant force) exerted by the two liquids.Weight of the cylinder = $V 	imes D 	imes g = (A/5) 	imes L 	imes D 	imes g$.Upthrust due to the upper liquid (density $d$): $F_1 = (A/5) 	imes (3L/4) 	imes d 	imes g$.Upthrust due to the lower liquid (density $2d$): $F_2 = (A/5) 	imes (L/4) 	imes 2d 	imes g$.Equating weight to total upthrust:$(A/5) 	imes L 	imes D 	imes g = (A/5) 	imes (3L/4) 	imes d 	imes g + (A/5) 	imes (L/4) 	imes 2d 	imes g$.Dividing both sides by $(A/5) 	imes L 	imes g$:$D = (3/4)d + (1/4) 	imes 2d = (3/4)d + (2/4)d = (5/4)d$.Therefore,the density of the solid is $D = \frac{5}{4}d$.

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