Internal Structure and Density Practice

Sample questions

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1. Sample 1difficulty 1/5

   A block of aluminum has mass $540~\text{g}$ and volume $200~\text{cm}^3$. What is its density?

   • A

     $1.4~\text{g/cm}^3$

   • B

     $5.4~\text{g/cm}^3$

   • C

     $2.7~\text{g/cm}^3$

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   • D

     $27~\text{g/cm}^3$

   Why

   $\rho = m/V = 540/200 = 2.7~\text{g/cm}^3$ (matches aluminum).

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2. Sample 2difficulty 1/5

   A liquid of mass $400~\text{g}$ fills $0.50~\text{L}$. Its density is

   • A

     $0.4~\text{g/cm}^3$

   • B

     $2.0~\text{g/cm}^3$

   • C

     $1.0~\text{g/cm}^3$

   • D

     $0.8~\text{g/cm}^3$

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   Why

   $\rho = m/V = 400/500 = 0.80~\text{g/cm}^3$ ($1~\text{L} = 1000~\text{cm}^3$).

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3. Sample 3difficulty 3/5

   A solid block weighs $20~\text{N}$ in air and $15~\text{N}$ when fully submerged in water. Its volume (using $\rho_w = 1000~\text{kg/m}^3$, $g \approx 10~\text{m/s}^2$) is

   • A

     $10^{-3}~\text{m}^3$

   • B

     $2 \times 10^{-3}~\text{m}^3$

   • C

     $1.5 \times 10^{-3}~\text{m}^3$

   • D

     $5 \times 10^{-4}~\text{m}^3$

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   Why

   Buoyancy: $F_B = 20 - 15 = 5~\text{N}$. $V = F_B/(\rho g) = 5/10000 = 5 \times 10^{-4}~\text{m}^3$.

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