A cylinder of radius 25 cm is filled with an ideal fluid and is connectedby a ho

Question

A cylinder of radius 25 cm is filled with an ideal fluid and is connectedby a hose to a second cylinder of radius 35 cm. A mass of 40 kg is placed on the top of the smaller cylinder.

1. If the height of the two cylinders is exactly the same, what mass should be placed on the second cylinder to balanced the system?

2. Unfortunately, you discover that the only extra mass you have is another 40 kg block! If you place the extra 40 kg block on the second cylinder, what is the height of the top of the second cylinder compared to the height of the first if the fluid is known to have a density of 550 kg/m^3?

Please explain answers. will rate high for correct answers. Thanks

Explanation / Answer

1)as the pressure should be same at bottom of both cylinders,

pressure on large cylinder =pressure on smaller cylinder= force/area = 40*9.8)/(pi*0.25^2) = 1997.45 pa

pressure on larger cylinder = ma/area = (m*9.8)/(pi*0.35^2) = 1997.45

so, mass on larger cylinder = 78.4 kg

2)If we 40 kg on larger cylinder,

pressure = (40*9.8)/(pi*0.35^2) = 1019.1 pa

where p0 =1997.45+ rho*g*h1 = 5390 h1

so,P0 = 1019.1 pa + rho*g*h2

5390h1+1997.45 = 1019.1+5390h2

h1-h2 = 0.18 m = 18.15 cm

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