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A liquid is poured into a cylindrical vessel of radius R, and the force exerted by the liquid on the base is F1. The same quantity of liquid is then transferred to a vessel having a uniform square cross-section of side R. The force on the base of the square vessel is F2. Ignoring atmospheric pressure, which relation is correct?
- F1 = pi*F2
- F1 = F2/pi
- F1 = sqrt(pi)*F2
- F1 = F2
Correct answer: F1 = F2
Solution
Force on the base = pressure * area = (rho*g*h)*A. The volume of liquid is V = h*A, so h = V/A and F = rho*g*(V/A)*A = rho*g*V. For both vessels (each with vertical walls) the same volume of liquid is used, so the larger base area is exactly offset by the smaller liquid height. The force on the base therefore depends only on the volume and equals the weight of the liquid: F1 = F2.
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