- #1
brotherbobby
- 618
- 153
- Homework Statement
- Both liquid columns stand to a height ##h## in the diagram below, but the second has a block of wood floating in it. How does the gauge pressure at the point marked ##\mathbf A## differ from the gauge pressure at ##\mathbf B##?
- Relevant Equations
- Gauge pressure at a depth ##h## inside a liquid is given by : ##P_G = \rho_L gh##, where ##\rho_L## is the density of the liquid.
My answer : Both pressures are equal, i.e. ##\boxed{P_A = P_B}##.
Reason : (1) The block of wood displaces an amount (mass) of liquid equal to its weight (archimedes' principle for floating bodies, or law of floatation). Hence we can imagine removing the block in the second case and filling it up by water equal to the block's weight. Water would stand to the same height in both the liquid columns and the pressures at A and B would be the same.
The same can be shown in a different way, keeping the block in place.(2)
Is my answer correct?
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