NEET-XII-Physics
46: The Nucleus
- #2A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 × 1030 kg (twice the mass of the sun).Ans : Given:
Mass of the neutron star, M = 4.0 × 1030 kg
Density of nucleus, d = 2.4`` \times ``1017`` {}^{}``
Density of nucleus, `` d=\frac{M}{V}``
Here, V is the volume of the nucleus.
`` \therefore V=\frac{M}{d}=\frac{4\times {10}^{30}}{2.4\times {10}^{17}}``
`` =\frac{1}{0.6}\times {10}^{13}``
`` =\frac{1}{6}\times {10}^{14}``
`` ``
If R is the radius, then the volume of the neutron star is given by
`` V=\frac{4}{3}\pi {R}^{3}``
`` \therefore \frac{1}{6}\times {10}^{14}=\frac{4}{3}\times \,\mathrm{\,\pi \,}\times {R}^{3}``
`` \Rightarrow {R}^{3}=\frac{1}{6}\times \frac{3}{4}\times \frac{1}{\,\mathrm{\,\pi \,}}\times {10}^{14}``
`` \Rightarrow {R}^{3}=\frac{1}{8}\times \frac{100}{\,\mathrm{\,\pi \,}}\times {10}^{12}``
`` \therefore R=\frac{1}{2}\times {10}^{4}\times 3.17``
`` =1.585\times {10}^{4}=15\,\mathrm{\,km\,}``
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