The answer is not 0.0693 kg/m^3. Kindly help out with this. A plastic \'\'boat\'

Question

The answer is not 0.0693 kg/m^3. Kindly help out with this.

A plastic ''boat'' with a 25 cm^2 square cross section floats in a liquid. One by one, you place 50-g masses inside the boat and measure how far the boat extends below the surface. Your data are as follows: Graphing either m versus d or d versus m gives a straight line. In the graph shown above, we chose to plot d on the vertical axis and m on the horizontal axis. From the equation for the line of best fit given, determine the density p of the liquid Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

M = mass of the boat

for m = 0

d1 = 0.01 m

buoyancy force = Fb1 = D*A*d1*g = M*g

for m = 50g

d2 = (0.374*0.05)+0.01 = 0.0287 m

Fb2 = D*A*d2*g =(M+m)*g

therefore

Fb2 - Fb1

D*A*(d2-d1) = m

D = m/(A*(d2-d1))

D = 0.05/(0.0025*(0.0287-0.01))

D = 1069.52 kg/m^3   <<-----answer

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