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ISRO Technical Assistant Physics — practice by topic

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Fluid Statics (23)Thermodynamics (2)

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Density compares two measurable properties of a sample of matter. Which statement defines it?Read the answer and worked solution →Density is mass per unit volume. Which unit is therefore the SI unit of density?Read the answer and worked solution →A reservoir has a surface area of 50.0 km^2 and an average depth of 40.0 m. Taking the density of water as 1.00 x 10^3 kg/m^3, what mass of water does it hold?Read the answer and worked solution →Pressure is defined from a force and the surface on which that force acts. Which definition is correct?Read the answer and worked solution →

Worked practice questions

Density compares two measurable properties of a sample of matter. Which statement defines it?

  1. The weight per unit of surface area
  2. The volume per unit of mass
  3. The mass per unit of volume
  4. The force per unit of area
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Correct answer: C. The mass per unit of volume

1. Density is defined as the mass of a substance divided by the volume that mass occupies. 2. In symbols this is written as mass divided by volume, so density is the mass per unit of volume. 3. Volume per unit of mass is the reciprocal of density, not density itself. 4. Force per unit of area is the definition of pressure, and weight per unit of surface area is not a standard quantity here. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.2 Density_

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Density is mass per unit volume. Which unit is therefore the SI unit of density?

  1. Newtons per cubic metre
  2. Grams per cubic centimetre
  3. Kilograms per square metre
  4. Kilograms per cubic metre
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Correct answer: D. Kilograms per cubic metre

1. Density is mass divided by volume, so its unit is an SI mass unit divided by an SI volume unit. 2. The SI unit of mass is the kilogram and the SI unit of volume is the cubic metre. 3. The SI unit of density is therefore kilograms per cubic metre. 4. Grams per cubic centimetre is a convenient non-SI alternative, and a newton is a force rather than a mass. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.2 Density_

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A reservoir has a surface area of 50.0 km^2 and an average depth of 40.0 m. Taking the density of water as 1.00 x 10^3 kg/m^3, what mass of water does it hold?

  1. 2.00 x 10^9 kg
  2. 2.00 x 10^6 kg
  3. 2.00 x 10^12 kg
  4. 2.00 x 10^15 kg
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Correct answer: C. 2.00 x 10^12 kg

1. Mass follows from density and volume, since density is mass divided by volume, so mass equals density times volume. 2. The volume of the reservoir is its surface area multiplied by its average depth. 3. Convert the area first: 1 km is 10^3 m, so 1 km^2 is 10^6 m^2 and 50.0 km^2 = 5.00 x 10^7 m^2. 4. Volume = (5.00 x 10^7 m^2)(40.0 m) = 2.00 x 10^9 m^3. 5. Mass = (1.00 x 10^3 kg/m^3)(2.00 x 10^9 m^3) = 2.00 x 10^12 kg. 6. The value 2.00 x 10^9 kg is the trap for anyone who reports the volume in cubic metres and forgets to multiply by the density. 7. Answers of 2.00 x 10^6 kg and 2.00 x 10^15 kg come from squaring the kilometre conversion wrongly, either by leaving the area in km^2 or by using 10^6 m per km. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.2 Density_

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