If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will b e ______ hours 30 minutes.

Question

G1 Physics · Accepted Answer

By conservation of angular momentum: I₁ω₁ = I₂ω₂ For a sphere: I ∝ MR² Mass remains constant and: R₂ = ( 3 4 \frac{3}{4} 4 3 ​ )R₁ Since: ω = 2π/T we have: R₁²/T₁ = R₂²/T₂ Therefore: T₂ = T₁(R₂/R₁)² = 24 × ( 3 4 \frac{3}{4} 4 3 ​ )² = 24 × 9/16 = 13.5 h = 13 h 30 min Hence the blank is: 13