Statement I :A If earth shrink (without change in mass) to half it’s present size. Length of the day would become 6 hours. Statement II: As size of earth changes its moment of inertia changes.

Question

Statement I :A If earth shrink (without change in mass) to half it’s present size. Length of the day would become 6 hours. Statement II: As size of earth changes its moment of inertia changes. (A) If both statement I and statement II are true and statement II is the correct explanation of statement I. (B) If both statement I and statement II are true but statement II is not the correct explanation of statement I. (C) If statement I is true but statement II is false. (D) If both statement I and statement II are false.

Tardigrade Admin · Accepted Answer

When earth shrinks its angular momentum remains constant i.e.,

L = I ω = \frac{2}{5} m R^{2} \times \frac{2 π}{T} = constant

T \propto I \propto R^{2}

it means if size of earth changes then it's moment of inertia changes.
If radius is half so time period will become

T /4

. Hence

24/4 = 6 Hr

Q. Statement I :A If earth shrink (without change in mass) to half it’s present size. Length of the day would become 6 hours. Statement II : As size of earth changes its moment of inertia changes.

If both statement I and statement II are true and statement II is the correct explanation of statement I.

If both statement I and statement II are true but statement II is not the correct explanation of statement I.

If statement I is true but statement II is false.

If both statement I and statement II are false.

When earth shrinks its angular momentum remains constant i.e., L=Iω=52​mR2×T2π​= constant T∝I∝R2 it means if size of earth changes then it's moment of inertia changes. If radius is half so time period will become T/4. Hence 24/4=6Hr

Q. Statement I :A If earth shrink (without change in mass) to half it’s present size. Length of the day would become 6 hours.
Statement II : As size of earth changes its moment of inertia changes.