Certain weight is attached with a spring. It is pulled down and then released. It oscillates up and down. Its K.E. will be

Options

A. maximum in the middle of the movement
B. maximum at the bottom
C. maximum just before it is released
D. constant

Answer

To determine where the kinetic energy (K.E.) of a weight attached to a spring is maximum during its oscillation, we can analyze the motion step by step.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a spring attached to a fixed point, and a weight (mass) is hung from the free end of the spring. When the weight is pulled down and released, it will oscillate up and down due to the restoring force of the spring.

**Hint**: Visualize the spring's behavior when weight is applied and released.

2. **Equilibrium Position**:
- When the weight is attached, the spring stretches to a new equilibrium position due to the weight of the mass. At this position, the forces acting on the mass (weight and spring force) are balanced.

**Hint**: Remember that the equilibrium position is where the spring force equals the weight of the mass.

3. **Displacement from Equilibrium**:
- If the weight is pulled down further and then released, it will move upwards due to the spring force. As it moves, it will pass through the equilibrium position.

**Hint**: Consider the motion of the mass as it moves from the maximum displacement back to the equilibrium position.

4. **Velocity and Kinetic Energy**:
- At the maximum displacement (either up or down), the velocity of the mass is zero, which means the kinetic energy is also zero.
- As the mass moves towards the equilibrium position, it accelerates, and its velocity increases. The kinetic energy increases as the velocity increases.

**Hint**: Recall that kinetic energy is given by the formula \( K.E. = \frac{1}{2}mv^2 \).

5. **Maximum Kinetic Energy**:
- The kinetic energy will be maximum when the mass passes through the equilibrium position because this is where the velocity is at its highest. After passing this point, the mass will start to decelerate as it moves towards the opposite extreme position.

**Hint**: Think about the relationship between velocity and kinetic energy; maximum velocity means maximum kinetic energy.

6. **Conclusion**:
- Therefore, the kinetic energy of the weight attached to the spring is maximum at the equilibrium position (the middle of the movement).

**Final Answer**: The kinetic energy will be maximum in the middle of the movement.