First slide

Fluid statics

Question

A hollow sphere of radius R is made of a metal whose specific gravity is $ρ$ . The sphere will float in water if the thickness of wall of the sphere is
(density of water is 1 gm/cc)

Moderate

A

$> \frac{R}{3 ρ}$
B

$= \frac{2 R}{3 ρ}$
C

$< \frac{R}{3 ρ}$
D

$< \frac{4 R}{3 ρ}$

Solution

$4 π R^{2} x ρ = \frac{4}{3} π R^{3} (ρ_{w})$ x →the thickness of the wall.
$\begin{array}{l} x ρ = \frac{R}{3} (ρ_{w} = 1) \\ x = \frac{R}{3 ρ} \end{array}$

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