First slide

Fluid statics

Question

A 0.5 kg block of brass (density; 8 x $10^{3} kg m^{- 3})$ is suspended from a string. What is the tension in the string if the block is completely immersed in water?
(g = l0 ${ms}^{- 2}$ )?

Moderate

A

5 N
B

$\frac{0.5}{8 \times 10^{3}} N$
C

$\frac{5}{8} N$
D

$[5 - \frac{5}{8}] N$

Solution

Volume of block = $\frac{0.5}{8 \times 10^{3}} m^{3}$
Volume of displaced water = $\frac{0.5}{8 \times 10^{3}} m^{3}$
Weight of displaced water = $\frac{0.5}{8 \times 10^{3}} 10^{3} \times 10 N$
= $\frac{5}{8} N$
This is equal to upward buoyant force.
Tension in string in actual weight less the upward buoyant force. So, tension is $[5 - \frac{5}{8}] N .$

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