A child is standing with folded hands at the center of a platform rotating about its central axis. The kinetic energy of the system is `K`. The child now stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

Options

A. `2 K`
B. `K//2`
C. `K//4`
D. `4 K`

Explanation

To solve the problem, we need to analyze the situation using the principles of rotational motion, particularly focusing on the conservation of angular momentum and the relationship between kinetic energy, moment of inertia, and angular velocity.

### Step-by-step Solution:

1. **Understanding the Initial Conditions**:
- Let the initial moment of inertia of the system (child + platform) be \( I_1 \).
- Let the initial angular velocity be \( \omega_1 \).
- The initial kinetic energy of the system is given as \( K \).
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