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A liquid contains 100 cm3 of water and 40 cm3 of ethanol. If the densities of water and ethanol are 1 g/cm3 and 0.78 g/cm3 respectively. Determine the density of the mixture. 2. The diagram below show

Physics

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SECTION A

  1. A liquid contains 100 cm3100 \, \text{cm}^3 of water and 40 cm340 \, \text{cm}^3 of ethanol. If the densities of water and ethanol are 1 g/cm31 \, \text{g/cm}^3 and 0.78 g/cm30.78 \, \text{g/cm}^3 respectively. Determine the density of the mixture.
  1. Calculate the mass of water (MwM_w).

    $$
    M_w = \rho_w \times V_w = 1 \, \text{g/cm}^3 \times 100 \, \text{cm}^3 = 100 \, \text{g}
    $$
    
  2. Calculate the mass of ethanol (MeM_e).

    $$
    M_e = \rho_e \times V_e = 0.78 \, \text{g/cm}^3 \times 40 \, \text{cm}^3 = 31.2 \, \text{g}
    $$
    
  3. Calculate the total mass of the mixture (MtotalM_{total}).

    $$
    M_{total} = M_w + M_e = 100 \, \text{g} + 31.2 \, \text{g} = 131.2 \, \text{g}
    $$
    
  4. Calculate the total volume of the mixture (VtotalV_{total}).

    $$
    V_{total} = V_w + V_e = 100 \, \text{cm}^3 + 40 \, \text{cm}^3 = 140 \, \text{cm}^3
    $$
    
  5. Calculate the density of the mixture (ρmixture\rho_{mixture}).

    $$
    \rho_{mixture} = \frac{M_{total}}{V_{total}} = \frac{131.2 \, \text{g}}{140 \, \text{cm}^3} = 0.937 \, \text{g/cm}^3
    $$
    The density of the mixture is $\boxed{\text{0.937 g/cm}^3\text{}}$.
    

    2. The diagram below shows a micrometer screw gauge. What is the reading in SI units?

  6. Read the main scale.

    The edge of the thimble is past the 5 mm5 \, \text{mm} mark.
    Main scale reading = 5.00 mm5.00 \, \text{mm}

  7. Read the thimble scale.

    The horizontal line aligns with the 25th25^\text{th} division.
    Thimble scale reading = 25×0.01 mm=0.25 mm25 \times 0.01 \, \text{mm} = 0.25 \, \text{mm}

  8. Calculate the total reading.

    Total reading = Main scale reading + Thimble scale reading = $5.00 \, mm + 0.
    
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