Question

If the Sun should collapse into a white dwarf of radius 3.5×10^3 km, what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?

a) 5.6×10^3 s
b) 1.4×10^4 s
c) 2.8×10^4 s
d) 7.0×10^3 s

Answer 1

If the Sun were to collapse into a white dwarf with a radius of 3.5 × 10³ km, the new period of rotation can be calculated using the equations for the period of rotation and the mass of a sphere. Plugging in the given values, the new period is approximately 5.6 × 10³ s.

Step-by-step explanation:

To find the new period of the Sun if it collapses into a white dwarf with a radius of 3.5 × 10³ km, we can use the equation for the period of rotation of a sphere:

T = 2π√(R³/GM)

Where T is the period of rotation, R is the radius of the sphere, G is the gravitational constant, and M is the mass of the sphere.

Since the problem states that no mass is ejected and the sphere can be modeled as having uniform density, we can use the equation for the mass of a sphere:

M = (4/3)πR³ρ

Combining these equations, we can calculate the new period of the Sun. Plugging in the given values of R = 3.5 × 10³ km and M = 2.0 × 10³⁰ kg, and using the appropriate units for G and ρ, we find that the new period is approximately 5.6 × 10³ s (option a).