Question

A solid weighs 15gf in air and 13 gf when completely immersed in a liquid of relative
density Find (i) volume of the solid and (ii) the relative density of solid.

Answer 1

ANSWER:

Volume of Solid is 2.5 cm³

EXPLANATION :

Given, weight of solid in air = 15 gf and = weight of solid in liquid = 13 gf.,

• Relative Density of liquid = 0.8

Therefore, Density of liquid = 0.8 g cm3 (i) Let V be the volume of the solid.

Weight of liquid displaced = Volume of liquid displaced x density of liquid x g

$\sf{= V \: x \: 0.8 \: g \: dyne} \\ \\ </p><p></p><p> \sf{= V \: x \: 0.8 \: gf}$

Loss in the weight of the solid when immersed in the liquid = 15 - 13 = 2 gf =

But the weight of liquid displaced is equal to the loss in weight of the solid when

immersed in liquid.

Therefore,

$\sf{ V x 0.8 = 2} \\ \\ \sf{or V = 20 0.8} \\ \\ </p><p></p><p> \sf{V = {cm}^{3} } \\ \\ </p><p></p><p></p><p> \sf{V = 2.5 {cm}^{3} }$

Answer 2

$\huge\bf\mathfrak\blue{✫}$$\huge\bf\mathfrak{Required\: Answer}$

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☆Vᴏʟᴜᴍᴇ ᴏғ sᴏʟɪᴅ ɪs 2.5 ᴄᴍ³

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$\bf\underline\mathfrak\blue{Step-by-Step\: Explanation :}$

★Given,

➪ Weight of solid in Air = 15 gf

➪ Weight of solid in Liquid = 13 gf

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$\bf\underline\mathfrak\blue{★We\: know\: that :}$

• Relative Density of Liquid = 0.8g

• Therefore, Density of liquid = 0.8 cm³

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★ Let's Start :

Let v be the volume of the solid.

Weight of liquid displaced = Volume of liquid displaced × Density of liquid × g

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ = V × 0.8 dyne.

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ = V × 0.8 gf

★Loss in the weight of the solid when immersed in Liquid =15-13

⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ = 2 gf

But the weight of liquid displaced is equal to the loss in weight of the solid.

When immersed in liquid.

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★ Therefore,

V × 0.8 = 2

⠀ ⠀(or)

V = 200.8

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$\bf\underline\mathfrak\blue{★We\: know\: that :}$

V = cm³

V = 2.5 cm³

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