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Fundamentals Of Physics
Found in: Page 1303

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Short Answer

A neutron star is a stellar object whose density is about that of nuclear matter, 2×1017 kg/m3 . Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?

The value of the radius of the star is 13 km.

See the step by step solution

Step by Step Solution

Step 1: Given data

The density of the nuclear matter, p=2×1017kg/m3

Mean density of Sun according to Appendix C, ps=1410×1017kg/m3

Mean radius of Sun according to Appendix C, Rs=6.96×108m

Step 2: Understanding the concept of density  

As per the given concept, the Sun is to collapse to form into a star whose density is given. Thus, keeping the mass constant and relating this to the density, volume, and mass relation, we can get that the radius' cube value is inversely proportional to the density. Thus, using this proportionality relation, we can get the required value.


The density of a spherical object, p=m43πR3.......(1)

Step 3: Calculation of the radius of the star

From equation (1), we get that

p α1R3 with all other terms as costant.

R α1p1/3

Thus, using this above relation and the given data, we can get the radius of the star as follows:

R=Rspsp1/3 =6.96×108 m1410×1017 kg/m32×1017 kg/m31/3 =1.3×104 m =13 km

Hence, the value of the radius is 13 km.


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