Question

A piece of metal has a mass Of 200g in air, and 170g when Immersed In water Calculate It's Volume and density. (Density water is 1000 Kg/m3. Tako g= 9.8m/s2. ​

Answer 1

The volume and the density of the piece of metal are 3×10⁻⁵ m³ and 6666.67 kg/m³ respectively.

What is density?

Density can be defined as the ratio of mass and volume of an object.

To calculate the volume of the metal piece, we use the formula below.

Formula:

• Dw = [(m-m')g/Vg]............ Equation 1

Where:

• Dw = Density of water
• V = volume of water displaced by the metal = Volume of the metal piece.
• m = mass of the metal in the air
• m' = mass of the metal in water
• g = acceleration due to gravity.

Note: Recall from Archimedes' principle that an object will displace a volume of water that is equal to his own volume.

Make V the subject of the equation

• V = (m-m)/Dw............. Equation 2

From the question,

Given:

• Dw = 1000 kg/m³
• m = 200 g = 0.2 kg
• m' = 170 g = 0.17 kg
• g = 9.8 m/s²

Substitute these values into equation 2

• V = (0.2-0.17)/1000
• V = 0.03/1000
• V = 0.00003 m³
• V = 3×10⁻⁵ m³

To calculate the density of the metal piece, we use the formula below

Formula:

• D = m/V................ Equation 3

Where:

• D = Density of the metal piece
• m = mass of the metal piece in the air
• V = Volume of the metal piece.

Given:

• m = 200 g = 0.2 kg
• V = 0.00003 m³

Substitute these values into equation 3

• D = 0.2/(0.00003)
• D = 6666.67 kg/m³

Hence, The volume and the density of the piece of metal are 3×10⁻⁵ m³ and 6666.67 kg/m³ respectively.

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