The pressure, P, exerted on an underwater object can be determined
by this formula:
P = ρ g h
ρ is the density of water, which is 1000 kg/m3.
g is the acceleration caused by Earth’s gravity, which is 9.8 m/s2.
h is the depth of the object in the water in meters.
a. Determine the units of P by calculating the units resulting from the right side of the formula.

To determine the units of the pressure \( P \) from the given formula:

\[
P = \rho g h
\]

Let's break down each component:

### Step-by-Step Breakdown of Units:
1. **Density (\( \rho \)):** 
   - \( \rho \) is the density of water.
   - Given as \( 1000 \, \text{kg/m}^3 \).
   - Thus, the unit is:

   \[
   \text{kg/m}^3
   \]

2. **Acceleration due to Gravity (\( g \)):**
   - \( g \) is the acceleration caused by Earth's gravity.
   - Given as \( 9.8 \, \text{m/s}^2 \).
   - Thus, the unit is:

   \[
   \text{m/s}^2
   \]

3. **Depth (\( h \)):**
   - \( h \) is the depth of the object in the water.
   - Measured in meters (\( \text{m} \)).
   - Thus, the unit is:

   \[
   \text{m}
   \]

### Calculating the Units for Pressure (\( P \)):
Now, substitute the units of each component into the formula:

\[
P = \rho \cdot g \cdot h = (\text{kg/m}^3) \cdot (\text{m/s}^2) \cdot (\text{m})
\]

Simplify the expression:

1. Multiply the units:

   \[
   (\text{kg/m}^3) \cdot (\text{m}) = \text{kg/m}^2
   \]

2. Now include the unit for acceleration:

   \[
   (\text{kg/m}^2) \cdot (\text{m/s}^2) = \text{kg/(m \, s}^2)
   \]

### Final Unit for Pressure (\( P \)):
The resulting unit is:

\[
P = \text{kg/(m \, s}^2) = \text{N/m}^2
\]

This unit is known as the Pascal (\( \text{Pa} \)), which is the standard SI unit for pressure.

### Summary:
The units of pressure (\( P \)) are:

\[
\text{Pa} \quad \text{or} \quad \text{N/m}^2 \quad \text{or equivalently} \quad \text{kg/(m s}^2)
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How does changing the depth (\( h \)) affect the pressure exerted on an object underwater?
2. How would the pressure change if the object was in a liquid denser than water, like mercury?
3. What is the relationship between pressure and gravitational acceleration if we consider different planets?
4. How does atmospheric pressure influence the total pressure on an underwater object?
5. How do you convert pressure from Pascals to atmospheres?

**Tip:** Always remember that pressure in fluids increases linearly with depth due to the weight of the fluid above.

The pressure, P, exerted on an underwater object can be determined by this formula: P = ρ g h ρ is the density of water, which is 1000 kg/m3. g is the acceleration caused by Earth’s gravity, which is 9.8 m/s2. h is the depth of the object in the water in meters. a. Determine the units of P by calculating the units resulting from the right side of the formula.

Learn how to calculate the units of pressure (P) using the formula P = ρ g h, where ρ is the density of water, g is the gravitational acceleration, and h is the depth in meters. This problem is ideal for high school physics students, covering key concepts like dimensional analysis and Pascal's Law.

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