First slide

Fluid statics

Question

Spheres of iron and lead having same mass are completely immersed in water. Density of lead is more than that of iron. Apparent loss of weight is $W_{1}$ for iron sphere and $W_{2}$ for lead sphere. Then $W_{1} / W_{2}$ is

Moderate

A

1
B

between 0 and 1
C

zero
D

greater than 1

Solution

We know density $d = \frac{Mass (m)}{Volume (v)}$
For same mass, $d \propto \frac{1}{V}$
Since $d_{l} > d_{i}$ , we can conclude $V_{l} < V_{i}$
Now apparent loss of weight $W = ρ_{ω} . v . g$
$∴ \frac{W_{1}}{W_{2}} = \frac{ρ_{ω} . V_{i} . g}{ρ_{ω} . V_{l} . g} = \frac{V_{i}}{V_{l}} > 1$

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