Calculate the pressure due to the water.

The formula for hydrostatic pressure is $P = \rho g h$, where $\rho$ is the density of the liquid, $g$ is the acceleration due to gravity, and $h$ is the depth.

Given:

• Density of water ($\rho$) = $1000 \text{ kg/m}^3$
• Acceleration due to gravity ($g$) = $10 \text{ m/s}^2$
• Depth ($h$) = $20 \text{ m}$

Substitute the values into the formula:

$$P = (1000 \text{ kg/m}^3) \times (10 \text{ m/s}^2) \times (20 \text{ m})$$ $$P = 200000 \text{ Pa}$$

The pressure due to the water alone at this depth is $200,000 \text{ Pa}$.

The correct option is C.

$$\boxed{\text{C. } 200,000 \text{ Pa}}$$

Upthrust (buoyant force) is the difference between the weight of an object in air and its apparent weight when fully immersed in a fluid.

Given:

• Weight in air = $10.0 \text{ N}$
• Apparent weight in water = $7.0 \text{ N}$

Calculate the upthrust:

$$\text{Upthrust} = \text{Weight in air} - \text{Apparent weight in water}$$ $$\text{Upthrust} = 10.0 \text{ N} - 7.0 \text{ N}$$ $$\text{Upthrust} = 3.0 \text{ N}$$

The upthrust on the object is $3.0 \text{ N}$.

The correct option is B.

$$\boxed{\text{B. } 3.0 \text{ N}}$$

A liquid rises in a capillary tube due to surface tension. Surface tension causes the liquid to adhere to the walls of the tube and rise against gravity, forming a meniscus.

The correct option is B.

$$\boxed{\text{B. Surface tension}}$$

Terminal velocity is reached when the net force acting on the falling object becomes zero. At this point, the downward force (weight) is balanced by the upward forces (upthrust and viscous drag), resulting in zero acceleration.

The correct option is C.

$$\boxed{\text{C. The net force on the sphere is zero}}$$

Surface tension is the property of a liquid's surface that allows it to resist an external force due to the cohesive nature of its molecules. This property causes liquids to minimize their surface area. A soap bubble naturally takes on a spherical shape to minimize its surface area, which is a direct application of surface tension.

The correct option is C.

$$\boxed{\text{C. The spherical shape of a soap bubble}}$$

Pascal's principle states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. For a hydraulic press, this means the pressure on the small piston is equal to the pressure on the large piston.

$$P_1 = P_2$$ $$\frac{F_1}{A_1} = \frac{F_2}{A_2}$$

Where:

• $F_1$ = force on the small piston
• $A_1$ = area of the small piston
• $F_2$ = force on the large piston
• $A_2$ = area of the large piston

Given:

• $A_1 = 0.01 \text{ m}^2$
• $A_2 = 0.5 \text{ m}^2$
• $F_1 = 50 \text{ N}$

Rearrange the formula to solve for $F_2$:

$$F_2 = F_1 \times \frac{A_2}{A_1}$$

Substitute the given values:

$$F_2 = 50 \text{ N} \times \frac{0.5 \text{ m}^2}{0.01 \text{ m}^2}$$ $$F_2 = 50 \text{ N} \times 50$$ $$F_2 = 2500 \text{ N}$$

The force on the large piston is $2500 \text{ N}$.

The correct option is B.

$$\boxed{\text{B. } 2,500 \text{ N}}$$