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.

Answer 1

Answer: (A)

When earth shrinks its angular momentum remains constant i.e.,
$L=I \omega=\frac{2}{5} m R^{2} \times \frac{2 \pi}{T}=\text { constant }$
$T \propto I \propto R^{2}$ 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 $24 / 4=6 Hr$