First slide

Fluid statics

Question

A cylinder of mass M and average density d₁ is lowered into a vessel of cross-sectional area A, half full of liquid of density $d_{2} (d_{2} < d_{1}$ ) until it is completely covered. The increase in pressure at bottom of vessel is

Difficult

A

$\frac{M d_{2} g}{d_{1}}$
B

$\frac{{Md}_{2} g}{d_{1} A}$
C

$\frac{{Md}_{1} g}{d_{2}}$
D

$\frac{{Md}_{1} g}{d_{2} A}$

Solution

The volume of liquid displaced when the cylinder is immersed
$= \frac{M}{d_{1}}$
$Resultant upward thrust = \frac{M}{d_{1}} \times d_{2} g$
$∴ Thrust on liquid surface$
$= \frac{M}{d_{1}} \times d_{2} g (Newton's third law)$
This thrust is experienced by bottom
Increase of pressure at bottom
$= \frac{{Md}_{2} g}{d_{1} A}$

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