(a) Calculate the height of a water column which will exert on its base the same pressure as the 70 cm column of mercury. Density of mercury is `13.6 g cm^(-3)`
(b) Will the height of the water column in part (a) change if the cross section of the water column is made wider ?

Answer

To solve the problem step by step, let's break it down into two parts as given in the question.

### Part (a): Calculate the height of a water column which will exert the same pressure as a 70 cm column of mercury.

1. **Understand the formula for pressure**:
The pressure exerted by a column of liquid is given by the formula:
\[ P = \rho \cdot g \cdot h \]
where \( P \) is the pressure, \( \rho \) is the density of the liquid, \( g \) is the acceleration due to gravity, and \( h \) is the height of the liquid column.

2. **Identify the known values**:
- Height of mercury column, \( h_{Hg} = 70 \, \text{cm} \)
- Density of mercury, \( \rho_{Hg} = 13.6 \, \text{g/cm}^3 \)
- Density of water, \( \rho_{water} = 1 \, \text{g/cm}^3 \)

3. **Set up the equation**:
Since we want the pressure exerted by the water column to equal the pressure exerted by the mercury column, we can set up the equation:
\[ \rho_{water} \cdot g \cdot h_{water} = \rho_{Hg} \cdot g \cdot h_{Hg} \]

4. **Cancel out \( g \)**:
Since \( g \) is common on both sides, we can cancel it out:
\[ \rho_{water} \cdot h_{water} = \rho_{Hg} \cdot h_{Hg} \]

5. **Substitute the known values**:
Substitute the values into the equation:
\[ 1 \cdot h_{water} = 13.6 \cdot 70 \]

6. **Calculate \( h_{water} \)**:
\[ h_{water} = 13.6 \cdot 70 = 952 \, \text{cm} \]

Thus, the height of the water column that will exert the same pressure as a 70 cm column of mercury is **952 cm**.

### Part (b): Will the height of the water column in part (a) change if the cross-section of the water column is made wider?

1. **Understand the concept of pressure**:
The pressure exerted by a liquid column depends only on the height of the column and the density of the liquid, not on the cross-sectional area.

2. **Conclusion**:
Therefore, making the cross-section of the water column wider will not affect the height of the water column required to exert the same pressure. The height will remain **952 cm** regardless of the cross-section.

### Final Answers:
(a) The height of the water column is **952 cm**.
(b) No, the height of the water column will not change if the cross-section is made wider.