The new period will be 2.486 days.
What is the period?
The period is found as the ratio of the angular displacement and the angular velocity. Its unit is the second and is denoted by t. The value of time needed to complete the rotation is the total period.
Given data;
Mass of a star,m= 1.210×10³¹ kg
The time period for one rotation of the star, T = 20.30 days
D' = 0.350 D
R' = 0.350 R
From the law of conservation of angular momentum;
[tex]\rm I \omega = I' \omega' \\\\ \frac{2}{5} MR^2 \times \frac{2 \pi }{T}=\frac{2}{5} MR'^2 \\\\ R^2 \times \frac{1}{T}= R'^2 \times \frac{1}{T} \\\\ T' = \frac{R'^2T}{R^2} \\\\ T' = \frac{(0.350 R)^2 \times 26.1 }{R^2} \\\\T' = 0.1225 \times 20.30 \\\\ T'= 2.486 \ days[/tex]
Hence, the new period will be 2.486 days.
To learn more about the period, refer to the link;
https://brainly.com/question/569003
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