A solid sphere is rotating about a diameter at an angular velocity `omega`. If it cools so that its radius reduces to `I//n` of its original value, its angular velocity becomes

Options

A. `(omega)/(n)`
B. `(omega)/(n^(2))`
C. `omega n`
D. `n^(2) omega`

Explanation

To solve the problem, we need to apply the principle of conservation of angular momentum. Here's a step-by-step solution:

### Step 1: Understand the initial conditions
We have a solid sphere with an initial radius \( r \) and an initial angular velocity \( \omega \). The moment of inertia \( I_1 \) of the solid sphere about its diameter is given by the formula:
\[ I_1 = \frac{2}{5} m r^2 \]

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