SATHEE: Properties Of Solids And Liquids Question 263

Properties Of Solids And Liquids Question 263

Question: A hemispherical bowl just floats without sinking in a liquid ofdensity 1.2 × 103kg/m3. If outer diameter and the density of the bowl are 1 m and 2 × 104 kg/m3 respectively, then the inner diameter of the bowl will be [SCRA 1998]

Options:

A)0.94 m

B)0.97 m

C)0.98 m

D)0.99 m

Show Answer

Answer:

Correct Answer: C

Solution:

Weight of the bowl = mg= $V ρ g$

$= \frac{4}{3} π [{(\frac{D}{2})}^{3} - {(\frac{d}{2})}^{3}] ρ g$

where D = Outer diameter ,

d = Inner diameter $ρ$ = Density of bowlWeight of the liquid displaced by the bowl $= V σ g$

$= \frac{4}{3} π {(\frac{D}{2})}^{3} σ g$ where $σ$ is the density of the liquid.

For the flotation $\frac{4}{3} π {(\frac{D}{2})}^{3} σ g = \frac{4}{3} π [{(\frac{D}{2})}^{3} - {(\frac{d}{2})}^{3}] ρ g$

therefore ${(\frac{1}{2})}^{3} \times 1.2 \times 10^{3} = [{(\frac{1}{2})}^{3} - {(\frac{d}{2})}^{3}] 2 \times 10^{4}$

By solving we get d = 0.98 m.

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Properties Of Solids And Liquids Question 263

Question: A hemispherical bowl just floats without sinking in a liquid ofdensity 1.2 × 103kg/m3. If outer diameter and the density of the bowl are 1 m and 2 × 104 kg/m3 respectively, then the inner diameter of the bowl will be [SCRA 1998]

Options:

Answer:

Solution:

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