A hemispherical bowl just floats without sinking in a liquid of density 1200 kg/m³.if outer diametre of bowl is 1m and density of bowl is 20000 kg/m³ then inner diametre of bowl
Answers
The inner diametre of bowl is 0.98 m
Explanation:
=> It is given that,
Liquid of density, σ = 1200 kg/m³
Outer diameter, D = 1 m
Density of bowl, ρ = 20000 kg/m³
inner diametre of bowl, d = ?
=> According to law of floatation a body floats when,
weight of the body = weight of water displaced by bowl
∴ Wb = Ww
Vw * ρw * gw = Vb * σb *gb (∵ W = Vρg)
4/3 π * (D/2)³ σg = 4/3 π * [(D/2)³ - (d/2)³ ] ρg
(D/2)³ σ = 4/3 π * [(D/2)³ - (d/2)³ ] ρ
(1/2)³ * 1200 = [(1/2)³ - (d/2)³] * 20000
150 = 2500 (1 - d³)
0.06 = 1 - d³
d³ = 0.94
d = cube root (0.94) = 0.979
≈ 0.98 m
Thus, the inner diametre of bowl is 0.98 m
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