The Sun rotates once every 27 days. Assuming it remains a uniform-density sphere and doubles its radius without any external torque, calculate its new rotation period.
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Question

The Sun rotates once every 27 days. Assuming it remains a uniform-density sphere and doubles its radius without any external torque, calculate its new rotation period.

G1 Physics · Accepted Answer

Step 1: Absence of external torque implies angular momentum conservation: Iω = I′ω′. Step 2: Uniform solid sphere has moment of inertia I = (2/5)MR². Step 3: At unchanged mass, doubling radius gives I′ = (2/5)M(2R)² = 4I. Step 4: Therefore ω′ = ω/4. Since T = 2π/ω, the period becomes T′ = 4T. Step 5: T′ = 4 × 27 = 108 days. Final answer: 108 days, Option D.