Question

A 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 x 10³⁰ kg (twice the mass of the sun).

Answer 1

R = ½ x 10⁴ x 3.17 = 1.585x 10⁴ m = 15 km.

Comments

Hey! Here the density of neutron star will be 2.8×10^17. Then the exact answer 15 km will come.

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here, density of nucleus, d = 2.4 x 10^17.

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If density is 2.4 × 10^17, then the exact answer 15 will not come

Answer 2

Density of the neutron star = 2.8 × 10^17 kg/m^3

Mass of the neutron star = 4 × 10^30 kg

So, for volume of neutron star:

volume = mass / density

V = (4 × 10^30) ÷ (2.8 × 10^17)

V = 10/7 × 10^13

V = 1/7 × 10^14 cubic metres

Also, for radius of neutron star:

V = 4/3 × pi × r^3

4/3 × 22/7 × r^3 = 1/7 × 10^14

r^3 = 3.375 × 10^12 (approx.)

r = 1.5 × 10^4 metres

r = 1.5 × 10 kilometres

r = 15 km.

Hence, the radius of the neutron star is 15 km.

Answer 3

Given, 

Mass of neutron star, M = 4.0 x 10^30 kg

Density of nucleus, d = 2.4 x 10^17

Density of nucleus, d = M/V

Here, V is the volume of the nucleus.

If R is the radius, then the volume of the neutron star is given y

Comments

If we round off 1.585×10^4 m, it will be equal to 1.6×10^4m = 16 km.