Question

A piece of metal weighs 15.1 gm in air, 9.6 gm in water and 10.4 gm in liquid then the sp. gravity of the liquid is

Answer 1

Specific Gravity of the liquid is 0.85

Explanation:

Given:

Weight of the metal = 15.1 gram

Weight of metal in water = 9.6 gram

Weight of metal in liquid = 10.4 gram

To find out:

Specific gravity of the liquid

Solution:

Let the density of the metal be d

Then

Volume of the metal = Weight/Density = 15.1/d

When immersed in water, the metal will displace this volume of water

If density of water is dw

Then

Weight of water displaced = (15.1/d)dw

Therefore,

Weight of metal in water

= Weight of metal - Weight of water displaced

= 15.1 - (15.1/d)dw

According to the question

15.1 - (15.1/d)dw = 9.6

or, (15.1/d)dw = 5.5   ........... (1)

Similarly,

If the density of the liquid is dl

Then

Weight of metal in liquid

= Weight of metal - Weight of liquid displaced

= 15.1 - (15.1/d)dl

According to the question

15.1 - (15.1/d)dl = 10.4

or, (15.1/d)dl = 4.7    .................(2)

We have to find the specific gravity of the liquid i.e. dl/dw

Dividing eq (2) by eq (1)

dl/dw = 4.7/5.5 = 0.85

Therefore,

Specific gravity of the liquid is 0.85

Hope this answer is helpful.

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