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Relative density

A hollow sphere of external and internal diameter 4 cm and 2 c

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Hard

Solving time: 4 mins

A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5 $g c m^{- 3}$ . The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.

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A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5

g c m^{- 3}

. The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.

6 mins ago

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6 mins ago

Text solutionVerified

By applying the definition of density

ρ

, the mass

m

of a body can be written in terms of its volume

V

as:

m = ρ V

Mass of sphere

= ρ V

m = ρ \frac{4}{3} π (R_{2}^{3} - R_{1}^{3})

Where,

R_{2} = 4 cm

and

R_{1} = 2

m = \frac{4}{3} π ρ (4^{3} - 2^{3})

m = \frac{4}{3} π ρ (64 - 8)

m = \frac{224}{3} π ρ

Here, it is given that level of liquid coincides with the centre of the sphere. Thus, the volume of liquid displaced is half of the volume of the sphere.
The gravitational force on the body

=

The buoyant force on the body
Weight of body

=

Weight of liquid displaced

m g = ρ_{l} V_{l} g

(\frac{224}{3} π ρ) g = (3.5) (\frac{1}{2} \times \frac{4}{3} π \times R_{2}^{3}) g

224 ρ = 7 \times 4^{3}

ρ = 2 g cc

ρ = 2 \times 1 0^{3} kgm^{- 3}

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Question Text	A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5 $g c m^{- 3}$ . The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.
Topic	Gravitation
Subject	Science
Class	Class 9
Answer Type	Text solution:1
Upvotes	77

A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5 $g c m^{- 3}$ . The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.

Text solutionVerified

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A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5 gcm−3. The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.

Text solutionVerified

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A hollow sphere of external and internal diameter 4 cm and 2 cm, respectively, floats in a liquid of density 3.5 $g c m^{- 3}$ . The level of the liquid coincides with the center of the sphere. Calculate the density of the material of the sphere.