If the Earth suddenly shrinks to 1/64 of its original volume with its mass unchanged, its rotation period becomes 24/x hours. Find x.
Physics · Circular Motion
JEE Mains 10 April 2023 Shift 1 Morning Shift

Question

If the Earth suddenly shrinks to 1/64 of its original volume with its mass unchanged, its rotation period becomes 24/x hours. Find x.

G1 Physics · Accepted Answer

Volume is proportional to R³. If volume becomes 1/64, radius becomes R' = R/4 With no external torque, angular momentum is conserved: I₁ω₁ = I₂ω₂ For a sphere, I ∝ MR². Since mass is unchanged, R²ω₁ = (R/4)²ω₂ Therefore, ω₂ = 16ω₁ Since T ∝ 1/ω, T₂ = T₁/16 = 24/16 hours Thus x = 16. Final value: 16