Answer:
a)  w = 2.52 10⁷ rad / s, b)  K / K₀ = 1.19 10⁴
Explanation:
a) We can solve this exercise using the conservation of angular momentum.
Initial instant. Before collapse
          L₀ = I₀ w₀
Final moment. After the collapse
          L_f = I w
angular momentum is conserved
         L₀ = L_f
          I₀ w₀ = I w                 (1)
          
The moment of inertia of a sphere is
         I = 2/5 m r²
we take from the table the mass and diameter of the star
         m = 1,991 10³⁰ kg
         r₀ = 6.96 10⁸ m
         r = 6.37 10⁶ m
to find the angular velocity let's use
        w = L / T
where the length of a circle is
       L = 2π r
       T = 24 days (24 h / 1 day) (3600 s / 1h) = 2.0710⁶ s
we substitute
       w = 2π r / T
       wo = 2π 6.96 10⁸ / 2.07 10⁶
       wo = 2.1126 10³ rad / s
we substitute in equation 1
       w =  
       w = 2/5 mr₀² / 2/5 m r² w₀
       w = ( ) ² wo
) ² wo
       w = (6.96 10⁸ / 6.37 10⁶) ² 2.1126 10³
       w = 2.52 10⁷ rad / s
b) the kinetic energy ratio
       K = ½ m w²
        K₀ = ½ m w₀²
        K = ½ m w²
        K / K₀ = (w / wo) ²
        K / K₀ = 2.52 10⁷ / 2.1126 10³
        K / K₀ = 1.19 10⁴