Question

If the earth suddenly contracts to \((\frac{1}{3})^{rd}\) of its present size without change in its mass, the ratio kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself)

• A. \(9\)
• B. \(5\)
• C. \(7\)
• D. \(6\)

Hint:

L is conserved, so K is proportional to 1/I.

Answer 1

The Correct Option is A

Step 1: Use omega:
Since $I\omega$ is constant and $I$ falls to $\frac19$, $\omega'=9\omega$.

Step 2: Compute KE:
$K=\frac12I\omega^2$. After: $\frac12\cdot\frac I9\cdot81\omega^2=9\cdot\frac12I\omega^2$.

Step 3: Ratio:
$K'/K=9$. Option (A).

Final Answer:
Omega becomes 9 times and I becomes 1/9. \[ \boxed{A} \]