Q1. What is the total pressure at the bottom of a cylindrical container full of alcohol (density 810 kg/m³), with a diameter of 10 m and a depth of 5 m?

Background

Topic: Fluid Statics (Hydrostatic Pressure)

This question tests your understanding of how to calculate the pressure at the bottom of a fluid column, considering both atmospheric and hydrostatic pressure.

Key Terms and Formulas

• Hydrostatic Pressure:

• = atmospheric pressure (usually 1.01 × 105 Pa unless otherwise specified)

• = density of the fluid (kg/m³)

• = acceleration due to gravity (9.8 m/s²)

• = depth of the fluid (m)

Step-by-Step Guidance

1. Identify the known values: kg/m³, m, m/s², Pa.

2. Calculate the hydrostatic pressure due to the alcohol: .

3. Add the atmospheric pressure to the hydrostatic pressure: .

Try solving on your own before revealing the answer!

Q2. Suppose you add 10 liters of fluid (density 1,000 kg/m³) to a large open cylindrical tank of radius 1 m. What is the rise in depth of the fluid?

Background

Topic: Volume and Geometry in Fluid Statics

This question tests your ability to relate the volume of fluid added to the change in height in a cylindrical container.

Key Terms and Formulas

• Volume of a cylinder:

• = volume added (m³)

• = radius of the tank (m)

• = change in height (m)

Step-by-Step Guidance

1. Convert the volume from liters to cubic meters: $10= 0.01$ m³.

2. Set up the formula for the change in height: .

3. Rearrange to solve for : .

Try solving on your own before revealing the answer!

Q3. A rectangular block of copper (density 8,900 kg/m³) with dimensions 0.1 m × 0.1 m × 0.3 m is floating in water (density 1,000 kg/m³). What is the fraction of the block submerged?

Background

Topic: Buoyancy and Archimedes' Principle

This question tests your understanding of how to calculate the fraction of a floating object's volume that is submerged based on densities.

Key Terms and Formulas

• Buoyant force equals weight of displaced fluid:

• Weight of block:

• Fraction submerged:

Step-by-Step Guidance

1. Calculate the density ratio: .

2. Set up the formula for fraction submerged: .

3. Plug in the values for copper and water densities.

Try solving on your own before revealing the answer!

Q4. A spherical piece of plastic of radius 10 cm and density 750 kg/m³ is completely submerged in water and held by a string. What is the tension in the string?

Background

Topic: Buoyancy, Forces in Fluids

This question tests your ability to calculate the tension in a string holding a submerged object, considering buoyant force and weight.

Key Terms and Formulas

• Buoyant force:

• Weight of object:

• Tension:

• Volume of sphere:

Step-by-Step Guidance

1. Calculate the volume of the sphere: with m.

2. Calculate the weight of the plastic: .

3. Calculate the buoyant force: .

4. Set up the tension formula: .

Try solving on your own before revealing the answer!

Q5. Water flows through a pipe that has a radius of 5 cm and the water has a speed of 2 m/s. What is the volume flow rate of the water in the pipe?

Background

Topic: Fluid Dynamics (Continuity Equation)

This question tests your ability to calculate the volume flow rate using the area and velocity of the fluid.

Key Terms and Formulas

• Volume flow rate:

• Area of circle:

• = velocity (m/s)

Step-by-Step Guidance

1. Calculate the area of the pipe: with m.

2. Multiply the area by the velocity to get the volume flow rate: .

Try solving on your own before revealing the answer!

Q6. The sound from a jack hammer has a sound intensity level of 90 dB at a distance of 30 m. What is the sound intensity?

Background

Topic: Sound Intensity and Decibels

This question tests your ability to convert sound intensity level (dB) to actual intensity (W/m²).

Key Terms and Formulas

• Sound intensity level:

• = reference intensity ( W/m²)

• = sound intensity level (dB)

• = sound intensity (W/m²)

Step-by-Step Guidance

1. Set up the formula: .

2. Plug in the values for and .

3. Solve for by rearranging the formula.

Try solving on your own before revealing the answer!