Mass Weight And Density

Mass & Weight

• Mass is a measure of the quantity of matter in an object. It resists changes in motion and is a scalar quantity measured in kilograms (kg).
• Weight is a gravitational force on an object with mass. It is a vector quantity measured in newtons (N).
• Mass stays the same everywhere; weight changes with gravitational field strength.

Which statement correctly distinguishes mass and weight?

• Mass is a force; weight is a scalar
• Mass is measured in newtons; weight in kilograms
• Mass is the amount of matter; weight is a gravitational force
• Mass changes with location; weight is constant

Weight & Gravitational Field Strength

• Weight is the force acting on a mass in a gravitational field: $W = m \times g$.
• g is the gravitational field strength, measured in N/kg. On Earth, $g = 9.8 N/kg$.
• An object's weight changes if g changes (e.g., on the Moon $g = 1.6 N/kg)$, but its mass remains the same.

The weight of a 5.0 kg object on Earth $(g = 9.8 N/kg)$ is ____ N.

Density

• Density is the mass per unit volume of a material: ρ $= m / V$.
• Units: $kg/m^{3}$ or $g/cm^{3}$. $1 g/cm^{3} = 1000 kg/m^{3}$.
• Low-density objects (e.g., feathers) have less mass for the same volume than high-density objects (e.g., metal).

A cube of side 2 cm has mass 16 g. What is its density?

• $2 g/cm^{3}$
• $4 g/cm^{3}$
• $8 g/cm^{3}$
• $16 g/cm^{3}$

Measuring Density of Regular Solids

• Use a digital balance to measure mass.
• Measure dimensions (length, width, height) with a ruler, vernier calipers, or micrometer.
• Calculate volume using appropriate formula $(e.g., V =$ length × width × height for a cuboid).
• Repeat measurements and take averages to reduce random error.

Which statements about measuring density are correct?

• A digital balance measures mass.
• Volume of a regular solid can be found by displacement.
• Repeat readings help reduce random errors.
• The density of a liquid is found by measuring its mass and volume.

Measuring Density of Irregular Solids

• Use a eureka (displacement) can filled with water just below the spout.
• Place an empty measuring cylinder under the spout.
• Lower the object gently into the can; collect displaced water.
• Volume of displaced water equals volume of the object.
• Density = mass / volume.

An irregular object has mass 50 g. It displaces $20 cm^{3}$ of water. Its density is ____ g/cm^{3}.

Floating and Sinking

• An object floats if its density is less than the fluid's density; it sinks if denser.
• Upthrust is an upward force on a submerged object, opposite to weight.
• If upthrust equals weight, the object floats; if upthrust < weight, it sinks.
• The denser the fluid, the greater the upthrust.

A block of wood $(density 0.8 g/cm^{3})$ is placed in water $(density 1.0 g/cm^{3})$. What happens?

• It sinks because it is less dense than water
• It floats because it is less dense than water
• It sinks because it is more dense than water
• It floats because it is more dense than water

Factors Affecting Floating & Sinking

• If density of object > density of fluid → sink.
• If density of object < density of fluid → float.
• If upthrust = weight → float; if upthrust < weight → sink.
• Upthrust depends on fluid density and volume of fluid displaced.

Potassium $(density 0.862 g/cm^{3})$ must sink in mineral oil. Which oil should be used?

• Oil $A: 0.864 g/cm^{3}$
• Oil $B: 0.890 g/cm^{3}$
• Oil $C: 0.825 g/cm^{3}$
• Oil $D: 0.880 g/cm^{3}$

Key Equations Summary

• Weight: $W = m \times g (g = 9.8 N/kg$ on Earth).
• Density: ρ $= m / V$.
• Volume of cuboid: $V =$ length × width × height.
• Volume of sphere: $V = \frac{4}{3} \pi$ r³; cylinder: $V = \pi r^{2} h$.

The weight of a 3.0 kg object on Earth $(g = 9.8 N/kg)$ is ____ N.

Practical Tips for Density Experiments

• Zero the digital balance before each measurement.
• For irregular objects, lower gently to avoid splashing.
• Take repeat readings and calculate averages.
• Handle glassware carefully; avoid spills on electrical balances.

Which are correct safety/accuracy measures?

• Zero the balance before measuring mass.
• Drop the irregular object quickly into the can.
• Take only one measurement to save time.
• Use a ruler for small lengths to improve precision.