Which of the following statements are correct when a gymnast sitting o...
The correct answer is option A) 2 and 3.
Explanation:
When a gymnast sitting on a rotating stool with his arms outstretched suddenly lowers his hands, several changes occur in the system. Let's analyze each statement and its correctness:
1. The angular velocity decreases: This statement is incorrect. According to the law of conservation of angular momentum, the total angular momentum remains constant if no external torque is applied. When the gymnast lowers his hands, his moment of inertia decreases, but angular velocity increases to conserve angular momentum.
2. The angular velocity increases: This statement is correct. As mentioned above, when the gymnast lowers his hands, his moment of inertia decreases. According to the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity, if I decreases, ω must increase to keep the angular momentum constant.
3. The moment of inertia decreases: This statement is correct. The moment of inertia depends on the distribution of mass and how it is arranged with respect to the axis of rotation. When the gymnast lowers his hands, he brings his mass closer to the axis of rotation, reducing the moment of inertia.
4. The moment of inertia increases: This statement is incorrect. Lowering the hands brings the mass closer to the axis of rotation, reducing the moment of inertia.
Therefore, the correct statements are 2 and 3: The angular velocity increases, and the moment of inertia decreases.