The restoring force in the case of a column of mercury in a U-tube is provided by the weight of the mercury. Let's understand this in detail.

Restoring Force in Simple Harmonic Motion (SHM):
In simple harmonic motion, the restoring force is responsible for bringing the object back to its equilibrium position. It is directly proportional to the displacement of the object from the equilibrium position and acts in the opposite direction to the displacement.

Explanation:
In the case of a column of mercury in a U-tube, the restoring force is provided by the weight of the mercury. Here's how it works:

1. U-Tube Setup:
- The U-tube consists of a long vertical tube filled with mercury.
- The tube is bent into a U-shape, with one end open to the atmosphere and the other end connected to a vacuum or an air-tight chamber.

2. Equilibrium Position:
- In the equilibrium position, the mercury in both arms of the U-tube is at the same height.
- The pressure exerted by the atmosphere on the open end of the tube is equal to the pressure exerted by the mercury column in the other arm.

3. Displacement from Equilibrium:
- If the mercury column in one arm of the U-tube is raised or lowered, it creates a displacement from the equilibrium position.
- Let's consider the case where the mercury column in one arm is raised.

4. Weight of the Mercury:
- The raised mercury column experiences an increased weight due to gravity.
- This weight of the mercury provides the restoring force in the system.

5. Restoring the Equilibrium:
- The weight of the raised mercury column acts in the opposite direction to the displacement.
- It exerts a downward force on the column, trying to bring it back to its original position.
- This restoring force increases as the displacement increases, following the characteristics of simple harmonic motion.

Therefore, in the case of a column of mercury in a U-tube, the weight of the mercury provides the restoring force required for simple harmonic motion.