Chapter 10, Problem 1QQ

To determine

The object which has the smallest radius.

Answer to Problem 1QQ

The white dwarf with $1.2M_{Sun}$ has the least radius of the given objects.

Explanation of Solution

Introduction:

When a low mass star reaches the end of its lifetime, it sheds its outer layers in the form of nebula. Its core stands exposed and this exposed core of the star is called the white dwarf.

A white dwarf has a very large gravity at its surface because they have masses equal to stars but a very small size. The star is kept in equilibrium due to a counter pressure called the electron degeneracy pressure, when the inward pressure due to gravity is countered by the outward degeneracy pressure.

It is found that the more the mass of the white dwarf, smaller is its size. This is because the large mass results in greater gravitational forces, which compress the star to a greater extent.

A white dwarf of mass equal to $1M_{Sun}$ has a radius almost equal to that of the Earth. This means that a 1.2 $M_{Sun}$ white dwarf should be smaller than the Earth. Therefore, the 0.6 $M_{Sun}$ white dwarf should be bigger than the 1.2 $M_{Sun}$ white dwarf.

Thus, option a is correct and b is incorrect.

Jupiter is the largest planet in the solar system with a radius of about 11.2 times the Earth radius, making it the largest of the given objects.

Thus, option c is incorrect.

Conclusion:

Of the objects-(a) 1.2 $M_{Sun}$ white dwarf, (b) a 0.6 $M_{Sun}$ white dwarf, or (c) Jupiter, the white dwarf with 1.2 $M_{Sun}$ has the least radius.