Q: A metal object weighs 2.0 kg in air and 1.5 kg when fully submerged in water. What is the buoyant force acting on the object?

$$F_B = (2.0 - 1.5) \times 9.8 = 4.9\, \text{N}$$

Q: A casserole dish has a mass of $$1555\, \text{g} in $$air and an apparent mass of $$880\, \text{g}$$ when fully submerged in water. What is the volume of the dish? (Assume $$g = 9.8\, \text{m/s}^2$$, $$\rho_{water} = 1000\, \text{kg/m}^3)$$

$$V = \frac{(1555 - 880) \times 10$$^{-3}$$}{1000} = 0.000675\, \text{m}^3$$

Question 1

A block of wood with density $$\$$rho_0$$ is floating in water with density $$\rho_{water}$$. If 30% of the block's volume is above the waterline, what is the density of the block?

Accepted Answer

$$\$$rho_0$$ = 0.7\, \rho_{water}$$

Question 2

A cube of side length $$d is $$fully submerged in a fluid of density $$\rho. $$What is the expression for the buoyant force $$F_B$$ acting on the cube?

Accepted Answer

$$F_B = \rho d^3$ g$$

Question 3

A helium balloon rises in air because:

Accepted Answer

The density of helium is less than the density of air, so the buoyant force exceeds the weight of the balloon.

Question 4

A metal object weighs 2.0 kg in air and 1.5 kg when fully submerged in water. What is the buoyant force acting on the object?

Accepted Answer

$$F_B = (2.0 - 1.5) 	imes 9.8 = 4.9\, 	ext{N}$$

Question 5

A plastic block floats in water with 80% of its volume submerged. If the density of water is $$1000\, 	ext{kg/m}^3$$, what is the density of the block?

Accepted Answer

$$800\, 	ext{kg/m}^3$$

Question 6

Which statement best describes Archimedes' principle?

Accepted Answer

The buoyant force on an object is equal to the weight of the fluid displaced by the object.

Question 7

A bird's hollow bones are an evolutionary adaptation that helps it fly because:

Accepted Answer

Hollow bones decrease the bird's density, increasing the buoyant force from air.

Question 8

A block is fully submerged in a fluid. Which of the following correctly describes the pressure difference between the top and bottom surfaces of the block?

Accepted Answer

The pressure at the bottom is greater than at the top, resulting in a net upward force.

Question 9

A casserole dish has a mass of $$1555\, 	ext{g} in $$air and an apparent mass of $$880\, 	ext{g}$$ when fully submerged in water. What is the volume of the dish? (Assume $$g = 9.8\, 	ext{m/s}^2$$, $$ho_{water} = 1000\, 	ext{kg/m}^3)$$

Accepted Answer

$$V = \frac{(1555 - 880) 	imes 10$$^{-3}$$}{1000} = 0.000675\, 	ext{m}^3$$

Question 10

If an object is neutrally buoyant in a fluid, which of the following must be true?

Accepted Answer

The density of the object equals the density of the fluid.

Question 11

A ping-pong ball with diameter $$40\, 	ext{mm}$$ and negligible mass is placed inside a casserole dish that is fully submerged in water. If the dish has a mass of $$1555\, 	ext{g} in $$air and $$880\, 	ext{g}$$ apparent mass in water, how many ping-pong balls are needed to make the dish float? (Assume $$ho_{water} = 1000\, 	ext{kg/m}^3)$$

Accepted Answer

Approximately 10 balls

Question 12

Which of the following best explains why a beach ball is difficult to push underwater?

Accepted Answer

The buoyant force from the water is greater than the weight of the beach ball.

Question 13

An object is placed in a fluid and sinks to the bottom. Which statement is true?

Accepted Answer

The object's density is greater than the fluid's density.

Question 14

The apparent weight of an object in a fluid is less than its weight in air because:

Accepted Answer

The fluid exerts an upward buoyant force, reducing the net force measured by the scale.

Question 15

A block of volume $$V$$ and density $$\$$rho_0$$ is fully submerged in a fluid of density $$\rho$$. What is the condition for the block to float upward after being released?

Accepted Answer

$$\$$rho_0$$ \u003c \rho$$

Question 16

If the buoyant force on an object is less than its weight, what will happen when the object is released underwater?

Accepted Answer

It will sink to the bottom.

Question 17

Which equation correctly relates the buoyant force $$F_B to $$the mass $$m_{fluid} of $$the displaced fluid?

Accepted Answer

$$F_B = m_{fluid} g$$

Question 18

A submarine adjusts its density to match the density of seawater. What is the result?

Accepted Answer

The submarine achieves neutral buoyancy and remains at a constant depth.

Question 19

Which of the following is NOT a consequence of Archimedes' principle?

Accepted Answer

The pressure at the bottom of a submerged object is always less than at the top.

Question 20

A block of volume $$V$$ and mass $$m is $$floating in a fluid. Which equation relates the mass of the block to the volume of fluid displaced?

Accepted Answer

$$m = \rho_{fluid} V_{displaced}$$

Buoyant Force and Archimedes' Principle

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