A boy has a mass of 60, kg. He wants to swim | vedclass

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(D) According to the principle of flotation,for the boy and the log to float,the total weight of the system must be equal to the upthrust (buoyant for

Vedclass · Accepted Answer

$\frac{3}{20}\, m^3$

Vedclass · Answer

(D) According to the principle of flotation,for the boy and the log to float,the total weight of the system must be equal to the upthrust (buoyant force) exerted by the water.Let $V$ be the volume of the wooden log.Mass of the boy = $60\, kg$.Density of wood $ho_{wood} = 0.6 	imes 1000 = 600\, kg/m^3$.Density of water $ho_{water} = 1000\, kg/m^3$.Total weight of the system = Weight of boy + Weight of log$= 60g + (V 	imes 600)g$Upthrust (Buoyant force) = Weight of water displaced by the log$= V 	imes 1000 	imes g$Equating the two:$60g + 600Vg = 1000Vg$$60 = 1000V - 600V$$60 = 400V$$V = \frac{60}{400} = \frac{3}{20}\, m^3$.

$A$ boy has a mass of $60\, kg$. He wants to swim in a river with the help of a wooden log. If the relative density of the wood is $0.6$,what is the minimum volume of the wooden log required? (Density of river water is $1000\, kg/m^3$)

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