STATEMENT-1`:` Time period of the liquid executing S.H.M.in a U-tube depends on the area of cross section of U-tube.
and
STATEMENT-2 `:` The restoring force acting on liquid displaced from equilibrium position of U -tube depends on the difference in levels of liquid in the two limbs of U -tube.

Answer

To analyze the statements regarding the time period of a liquid executing simple harmonic motion (SHM) in a U-tube, we will break down the problem step by step.

### Step 1: Understanding the U-tube setup
A U-tube consists of two vertical limbs connected at the bottom. When a liquid is filled in the U-tube and displaced from its equilibrium position, it will oscillate back and forth, exhibiting simple harmonic motion (SHM).

### Step 2: Analyzing Statement 1
**Statement 1:** "The time period of the liquid executing SHM in a U-tube depends on the area of cross-section of the U-tube."

To determine if this statement is true or false, we need to derive the expression for the time period of the liquid in the U-tube.

1. When the liquid is displaced by a distance \( y \), the difference in height between the two limbs becomes \( 2y \).
2. The restoring force acting on the liquid can be expressed in terms of pressure difference caused by this height difference.
3. The restoring force \( F \) is given by:
\[ F = \Delta P \cdot A = \rho g (2y) \cdot A \]
where \( \Delta P \) is the pressure difference, \( A \) is the cross-sectional area, and \( \rho \) is the density of the liquid.
4. The mass \( m \) of the liquid column that is displaced can be expressed as:
\[ m = \rho \cdot A \cdot (L + y) \]
where \( L \) is the length of the liquid column.
5. The acceleration \( a \) can be expressed as:
\[ a = \frac{F}{m} = \frac{\rho g (2y) \cdot A}{\rho \cdot A \cdot (L + y)} = \frac{2g y}{L + y} \]
6. For small displacements, we can approximate \( L + y \approx L \), leading to:
\[ a \approx \frac{2g y}{L} \]
7. This shows that the motion is simple harmonic with angular frequency \( \omega^2 = \frac{2g}{L} \).
8. The time period \( T \) is given by:
\[ T = 2\pi \sqrt{\frac{L}{2g}} \]

From this derivation, we see that the time period \( T \) does not depend on the area of cross-section \( A \). Thus, **Statement 1 is false.**

### Step 3: Analyzing Statement 2
**Statement 2:** "The restoring force acting on the liquid displaced from the equilibrium position of the U-tube depends on the difference in levels of liquid in the two limbs of the U-tube."

1. The restoring force, as derived earlier, is directly proportional to the height difference \( 2y \) between the two limbs.
2. The greater the displacement \( y \), the greater the restoring force acting to bring the liquid back to its equilibrium position.

Thus, **Statement 2 is true.**

### Conclusion
- **Statement 1:** False (The time period does not depend on the area of cross-section).
- **Statement 2:** True (The restoring force depends on the difference in levels of liquid in the two limbs).