Neutron stars are believed to be composed of solid nuclear
matter, primarly neutrons.
Assuming that a neutron star has the same density as a neutron, calculate the mass (in kg ) of a small piece of a neutron star the size of a spherical pebib
with a radius of 0.14 mm .
Express your answer using two significant figures.

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UpStudy AI · Accepted Answer

To calculate the mass of a small piece of a neutron star with a spherical pebble radius of 0.14 mm, we'll follow these steps:

1. **Determine the Density of a Neutron Star:**
   - Neutron stars have an extremely high density, approximately $$ \rho = 1 \times 10^{18} $$ kg/m³.

2. **Convert the Radius to Meters:**
   $$
   r = 0.14 \, \text{mm} = 0.14 \times 10^{-3} \, \text{m} = 1.4 \times 10^{-4} \, \text{m}
   $$

3. **Calculate the Volume of the Sphere:**
   $$
   V = \frac{4}{3}\pi r^3 = \frac{4}{3} \times \pi \times (1.4 \times 10^{-4})^3
   $$
   $$
   V \approx \frac{4}{3} \times 3.1416 \times 2.744 \times 10^{-12} \, \text{m}^3 \approx 1.15 \times 10^{-11} \, \text{m}^3
   $$

4. **Calculate the Mass:**
   $$
   \text{Mass} = \rho \times V = 1 \times 10^{18} \, \text{kg/m}^3 \times 1.15 \times 10^{-11} \, \text{m}^3 = 1.15 \times 10^7 \, \text{kg}
   $$

5. **Express the Mass with Two Significant Figures:**
   $$
   \text{Mass} \approx 1.2 \times 10^7 \, \text{kg}
   $$

**Final Answer:**
The mass of the small piece is approximately 1.2 × 10⁷ kg.
The mass of the small piece is approximately $$1.2 \times 10^7$$ kg.

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