Deck 10: Fluids

Question 1

Choose the one alternative that best completes the statement or answers the question.
Substance A has a density of 3 g/cm³ and substance Bhas a density of 4 g/cm³. In order to obtain equal masses of these two substances, what must be the ratio of the volume of A to the volume of

A) $\frac { V A } { V B } = \sqrt { \frac { 3 } { 4 } }$
B) $\frac { V _ { \mathrm { A } } } { V _ { \mathrm { B } } } = \frac { 1 } { 3 }$
C) $\frac { V \mathrm {~A} } { V \mathrm {~B} } = \frac { 3 } { 1 }$
D) $\frac { V \mathrm {~A} } { V _ { \mathrm { B } } } = \frac { 3 } { 4 }$
E) $\frac { V _ { \mathrm { A } } } { V _ { \mathrm { B } } } = \frac { 4 } { 3 }$

Answer 1

E

Question 2

A compressed gas with a total mass of 107 kg is stored in a spherical container having a radius of 0.521 m. What is the density of the compressed gas?

A) $181 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $161 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $134 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $110 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Answer 2

A

Question 3

Choose the one alternative that best completes the statement or answers the question.
A spherical ball of lead $\text { (density } 11.3 \mathrm {~g} / \mathrm { cm } ^ { 3 } \text { ) }$ is placed in a tub of mercury $\left( \text { density } 13.6 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$
Which answer best describes the result?

A) The lead ball will float with about 17% of its volume above the surface of the mercury.
B) The lead will sink to the bottom of the mercury.
C) The lead ball will float with about 83% of its volume above the surface of the mercury.
D) The lead ball will float with its top exactly even with the surface of the mercury.

Answer 3

A

Question 4

Choose the one alternative that best completes the statement or answers the question.
When a box rests on a round sheet of wood on the ground, it exerts an average pressure $p$ on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure?

A) $2 p$
B) $p / 4$
C) $4 p$
D) $p \sqrt { 2 }$
E) $p / 2$

Question 5

Choose the one alternative that best completes the statement or answers the question.
A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is $\rho$ You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid. What is the density of the enlarged sphere?

A) $\rho / 8$
B) $\rho / 2$
C) $4 \rho$
D) $\rho$
E) $8 \rho$

Question 6

Choose the one alternative that best completes the statement or answers the question.
When a heavy metal block is supported by a cylindrical vertical post of radius R, it exerts a force F on the post. If the diameter of the post is increased to 2R , what force does the block now exert on the post?

A) F/2
B) $F / \sqrt { 2 }$
C) 2F
D) F/4
E) F

Question 7

Choose the one alternative that best completes the statement or answers the question.
If atmospheric pressure increases by an amount $\Delta p$ which of the following statements about the pressure in a lake is true? (There could be more than one correct choice.)

A) The absolute (total) pressure does not change.
B) The gauge pressure does not change.
C) The absolute (total) pressure increases by $\Delta p$
D) The absolute (total) pressure increases, but by an amount less than $\Delta p$
E) The gauge pressure increases by $\Delta p$

Question 8

Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is $Q = \frac { \Delta V } { \Delta t }$ what is the flow rate in pipe B ?

A) 4 Q
B) 8 Q
C) $Q \sqrt { 2 }$
D) 16 Q
E) 2 Q

Question 9

Write the word or phrase that best completes each statement or answers the question.
A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the absolute (total) pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

A)
B)
C)
D)
E)

Question 10

Write the word or phrase that best completes each statement or answers the question.
A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the buoyant force B on this block as a function of time t if the block just enters the water at time t = 0 s?

A)
B)
C)
D)
E)

Question 11

The density of material at the center of a neutron star is approximately $1.00 \times 10 ^ { 18 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ What is the mass of a cube of this material that is 1.76 microns on each side. (One micron is equal to $1.00 \times$ $\left. 10 ^ { - 6 } \mathrm {~m} . \right)$

A) 5.45 kg
B) 6.16 kg
C) 4.74 kg
D) 6.70 kg

Question 12

Choose the one alternative that best completes the statement or answers the question.
A styrofoam sphere of radius R has a density $\rho .$ You now carefully compress the sphere so its radius is R/2 . What is the density of the compressed sphere?

A) $8 \rho$
B) $4 \rho$
C) $\rho \sqrt { 2 }$
D) $\rho \sqrt { 8 }$
E) $2 \rho$

Question 13

Write the word or phrase that best completes each statement or answers the question.
A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the gauge pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

A)
B)
C)
D)
E)

Question 14

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest?

A) A
B) B
C) C
D) D
E) The pressure is the same at each of the labeled points.

Question 15

A plastic block of dimensions $2.00 \mathrm {~cm} \times 3.00 \mathrm {~cm} \times 4.00 \mathrm {~cm}$ has a mass of 30.0 g. What is its density?

A) $1.60 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
B) $1.20 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
C) $0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
D) $1.25 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

Question 16

A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

A) $3.63 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $7.26 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $1.37 \times 10 ^ { - 4 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $1.82 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 17

Under standard conditions, the density of air is $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ What is the mass of the air inside a room measuring $4.0 \mathrm {~m} \times 3.0 \mathrm {~m} \times 2.0 \mathrm {~m} ?$

A) 31 kg
B) 19 kg
C) 3.1 kg
D) 1.9 kg
E) 0.32 kg

Question 18

Two horizontal pipes have the same diameter, but pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe B is $Q = \frac { \Delta V } { \Delta t }$ what is the flow rate in pipe A ?

A) $Q \sqrt { 2 }$
B) 16Q
C) 4Q
D) 8Q
E) 2Q

Question 19

A $50 - \mathrm { cm } ^ { 3 }$ block of wood is floating on water, and a $50 - \mathrm { cm } ^ { 3 }$ chunk of iron is totally submerged in the water. Which one has the greater buoyant force on it?

A) the wood
B) Both have the same buoyant force.
C) the iron
D) It cannot be determined without knowing their densities.

Question 20

A round coin has a diameter of 19.55 mm , a thickness of 1.55 mm , and a mass of 2.50 g. What is its density?

A) $5.37 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $2.68 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $1.34 \times 10 ^ { 3 } \mathrm { kq } / \mathrm { m } ^ { 3 }$
D) $1.86 \times 10 ^ { - 4 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $21.5 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 21

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a large open tank contains a layer of oil $\text { (density } 450 \mathrm {~kg} / \mathrm { m } ^ { 3 } \text { ) }$
floating on top of a layer of water $\text { (density } \left. 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \right)$
that is 3.0 m thick, as shown in the sketch. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be $8.5 \times 10 ^ { 4 } \mathrm {~Pa} ?$

Question 22

One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. What net outward force is exerted on a square window of the house that is 2.03 m on each side? (1.00 atm= $\left. 1.01 \times 10 ^ { 5 } \mathrm {~Pa} \right)$

A) $5.19 \times 10 ^ { 4 } \mathrm {~N}$
B) $5.42 \times 10 ^ { 5 } \mathrm {~N}$
C) $4.82 \times 10 ^ { 5 } \mathrm {~N}$
D) $4.59 \times 10 ^ { 4 } \mathrm {~N}$

Question 23

Calculate the pressure exerted on the ground due to the weight of a 79-kg person standing on one foot. if the bottom of the person's foot is 13 cm wide and 28 cm long.

A) $2.1 \times 10 ^ { 4 } \mathrm {~Pa}$
B) $4.8 \times 10 ^ { 4 } \mathrm {~Pa}$
C) $5.3 \times 10 ^ { 4 } \mathrm {~Pa}$
D) $2.2 \times 10 ^ { 3 } \mathrm {~Pa}$

Question 24

A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $2.0 \times 10 ^ { 4 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
B) $3.9 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
C) $9.2 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) The question cannot be answered because the cross sectional area of the tank is needed.

Question 25

What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 44.0 cm at a depth of 9400 m in sea water? The density of sea water is 1025 $\mathrm { kg } / \mathrm { m } ^ { 3 }$

A) $2.87 \times 10 ^ { 11 } \mathrm {~N}$
B) $5.74 \times 10 ^ { 7 } \mathrm {~N}$
C) $2.87 \times 10 ^ { 7 } \mathrm {~N}$
D) $5.74 \times 10 ^ { 11 } \mathrm {~N}$
E) $1.83 \times 10 ^ { 7 } \mathrm {~N}$

Question 26

A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $570 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
The mass of the oil is closest to

A) 820
B) 210
C) 620
D) 1000
E) 410

Question 27

A container has a vertical tube, whose inner radius is 20.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $900 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
The density of the unknown liquid is closest to

A) $3600 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $3900 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $3100 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $3300 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $2800 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 28

A container has a vertical tube, whose inner radius is 12.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $320 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
The gauge pressure at level B is closest to

A) 790 Pa
B) 630 Pa
C) 310 Pa
D) 940 Pa
E) 470 Pa

Question 29

How many grams of ethanol $\left( \text { density } 0.80 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ should be added to 5.0 g of chloroform (density $\left. 1.5 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ if the resulting mixture is to have a density of $1.2 \mathrm {~g} / \mathrm { cm } ^ { 3 } ?$ Assume that the fluids do not change their volumes when they are mixed.

A) 1.8 g
B) 1.6 g
C) 2.4 g
D) 2.0 g
E) 4.4 g

Question 30

A cubical box 25.0 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.40 kPa and the pressure on the bottom surface is 112.00 kPa. What is the density of the fluid?

A) $1090 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $1120 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $1060 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $1030 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 31

The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $1.09 \times 10 ^ { 6 } \mathrm {~Pa}$
B) $1.09 \times 10 ^ { 3 } \mathrm {~Pa}$
C) $1.11 \times 10 ^ { 2 } \mathrm {~Pa}$
D) $1.16 \times 10 ^ { 6 } \mathrm {~Pa}$
E) $1.11 \times 10 ^ { 5 } \mathrm {~Pa}$

Question 32

The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of $1.04 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ calculate the absolute (total) pressure at the bottom of the trench in atmospheres. $\left( 1.00 \mathrm { in } = 2.54 \mathrm {~cm} , 1.00 \mathrm {~atm} = 1.01 \times 10 ^ { 5 } \mathrm {~Pa} \right)$

A) $1.1 \times 10 ^ { 6 } \text { atm }$
B) $1.1 \times 10 ^ { 8 } \mathrm {~atm}$
C) $1.1 \times 10 ^ { 3 } \text { atm }$
D) 2.1 atm
E) $1.1 \times 10 ^ { 5 } \mathrm {~atm}$

Question 33

Write the word or phrase that best completes each statement or answers the question.
A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density $0.820 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ If a 125-kg object is placed on the larger plate at A , how much mass should be placed on the smaller plate at B to balance it?.

Question 34

A circular window 30 cm in diameter in a submarine can withstand a net maximum force of $5.20 \times$ $10 ^ { 5 } \mathrm {~N}$ without damage. What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 1200 m
B) 750 m
C) 740 m
D) 680 m

Question 35

Choose the one alternative that best completes the statement or answers the question.
A 12,000-N car is raised using a hydraulic lift, which consists of a $U \text {-tube }$ with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the $\text { U-tube }$ has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons.

A) 727 N
B) 9265 N
C) 3.33 kN
D) 2.90 kN
E) 1.20 kN

Question 36

A 100-kg person sits on a 5-kg bicycle. The total weight is borne equally by the two wheels of the bicycle. The tires are 2.0 cm wide and are inflated to a gauge pressure of $8.0 \times 10 ^ { 5 } \mathrm {~Pa}$ What length of each tire is in contact with the ground?

A) 1.6 cm
B) 2.4 cm
C) 1.8 cm
D) 6.4 cm
E) 3.2 cm

Question 37

A person weighing 900 N is standing on snowshoes. Each snowshoe has area $2500 \mathrm {~cm} ^ { 2 }$ and has

A) $3600 \mathrm {~N} / \mathrm { m } ^ { 2 }$
B) $0.18 \mathrm {~N} / \mathrm { m } ^ { 2 }$
C) $1800 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) $0.36 \mathrm {~N} / \mathrm { m } ^ { 2 }$

Question 38

A brick weighs 50.0 N, and measures $30.0 \mathrm {~cm} \times 10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm}$
What is the maximum pressure it can exert on a horizontal surface due to its weight?

Question 39

The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the gauge pressure in the water at that point? The density of seawater is $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $2.22 \times 10 ^ { 8 } \mathrm {~Pa}$
B) $5.55 \times 10 ^ { 7 } \mathrm {~Pa}$
C) $8.88 \times 10 ^ { 7 } \mathrm {~Pa}$
D) $3.33 \times 10 ^ { 8 } \mathrm {~Pa}$
E) $1.11 \times 10 ^ { 8 } \mathrm {~Pa}$

Question 40

The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is $100 \mathrm {~cm} ^ { 2 } ?$

A) $2.9 \times 10 ^ { 5 } \mathrm {~Pa}$
B) $12 \times 10 ^ { 5 } \mathrm {~Pa}$
C) $2.9 \times 10 ^ { 4 } \mathrm {~Pa}$
D) $12 \times 10 ^ { 4 } \mathrm {~Pa}$

Question 41

Choose the one alternative that best completes the statement or answers the question.
A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 30 N
B) 40 N
C) 10 N
D) 70 N

Question 42

Write the word or phrase that best completes each statement or answers the question.
The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. Assume the pistons each have negligible weight.
(a) Determine the force that must be applied to the small piston.
(b) Determine the pressure applied to the fluid in the lift.

Question 43

Choose the one alternative that best completes the statement or answers the question.
A crane lifts a steel submarine of density $7800 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and mass 20,000 kg. What is the tension in the lifting cable (a) when the submarine is submerged in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and (b) when it is entirely out of the water?

A) $\text { (a) } 1.7 \times 10 ^ { 5 } \mathrm {~N} \text { (b) } 2.0 \times 10 ^ { 5 } \mathrm {~N}$
B) $\text { (a) } 2.6 \times 10 ^ { 3 } \mathrm {~N} \text { (b) } 2.0 \times 10 ^ { 5 } \mathrm {~N}$
C) $\text { (a) } 2.0 \times 10 ^ { 5 } \mathrm {~N} \text { (b) } 2.6 \times 10 ^ { 3 } \mathrm {~N}$
D) $\text { (a) } 2.0 \times 10 ^ { 5 } \mathrm {~N} \text { (b) } 1.7 \times 10 ^ { 5 } \mathrm {~N}$

Question 44

Choose the one alternative that best completes the statement or answers the question.
A 200-N object floats with three-fourths of its volume beneath the surface of the water. What is the buoyant force on the object? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 267 N
B) 200 N
C) 50 N
D) 150 N
E) It cannot be determined because we do not know the volume of the object.

Question 45

Choose the one alternative that best completes the statement or answers the question.
A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick. What is the minimum area of the floe that will just support the bear in saltwater of density $1030 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$ The density of ice is $980 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $2.0 \mathrm {~m} ^ { 2 }$
B) $4.0 \mathrm {~m} ^ { 2 }$
C) $3.0 \mathrm {~m} ^ { 2 }$
D) $1.0 \mathrm {~m} ^ { 2 }$

Question 46

Choose the one alternative that best completes the statement or answers the question.
A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$ What is its mass?

A) 150 g
B) 75 g
C) 38 g
D) 300 g

Question 47

Choose the one alternative that best completes the statement or answers the question.
In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight.

A) $2.9 \times 10 ^ { 3 } \mathrm {~N}$
B) $2.2 \times 10 ^ { 3 } \mathrm {~N}$
C) $5.0 \times 10 ^ { 3 } \mathrm {~N}$
D) $6.7 \times 10 ^ { 3 } \mathrm {~N}$

Question 48

Write the word or phrase that best completes each statement or answers the question.
A piece of aluminum with a mass of 1.0 kg and density of $2700 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
is suspended from a light cord and then completely immersed in a container of water having density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$
(a) Determine the volume of the piece of aluminum.
(b) Determine the tension in the cord when the aluminum is immersed in the container of water.

Question 49

Choose the one alternative that best completes the statement or answers the question.
An object has a volume of $4.0 \mathrm {~m} ^ { 3 }$ and weighs 40,000 N. What will its apparent weight be in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$

A) 9,800 N
B) 40,000 N
C) 39,200 N
D) 800 N

Question 50

Choose the one alternative that best completes the statement or answers the question.
When a container of water is placed on a laboratory scale, the scale reads 120 g. Now a 20-g piece of copper $\text { (of density } 8.9 \mathrm {~g} / \mathrm { cm } ^ { 3 } \text { ) }$
is suspended from a thread and lowered into the water, not touching the bottom of the container. What will the scale now read? The density of water is 1.0 $\mathrm { g } / \mathrm { cm } ^ { 3 }$

A) 120 g
B) 138 g
C) 122 g
D) 140 g

Question 51

Choose the one alternative that best completes the statement or answers the question.
An object floats with half its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 2000 N
B) 4000 N
C) 1000 N
D) It cannot be determined because we do not know the volume of the object.

Question 52

Choose the one alternative that best completes the statement or answers the question.
A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is $7860 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 34 N
B) 20 N
C) 40 N
D) 24 N
E) 2.5 N

Question 53

Choose the one alternative that best completes the statement or answers the question.
An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$ What is the density of the object?

A) $6000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $7000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $9000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $8000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 54

Choose the one alternative that best completes the statement or answers the question.
A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil with a density of $800 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? For purposes of this problem, neglect the weight of the pistons.

A) 1.88 kN
B) 3.67 kN
C) 1.20 kN
D) 0.954 kN
E) 1.96 kN

Question 55

Choose the one alternative that best completes the statement or answers the question.
What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $3.0 \times 10 ^ { - 4 } \mathrm {~N}$
B) $3.0 \times 10 ^ { - 5 } \mathrm {~N}$
C) 0.30 N
D) $3.0 \times 10 ^ { - 2 } \mathrm {~N}$

Question 56

Choose the one alternative that best completes the statement or answers the question.
A $1.00 - \mathrm { m } ^ { 3 }$ object floats in water with 20.0% of its volume above the waterline. What does the object weigh out of the water? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) 11,800 N
B) 7,840 N
C) 9,800 N
D) 1,960 N

Question 57

Choose the one alternative that best completes the statement or answers the question.
If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $10 ^ { 7 } \mathrm {~m} ^ { 3 }$
B) $10 ^ { 4 } \mathrm {~m} ^ { 3 }$
C) $10 ^ { 12 } \mathrm {~m} ^ { 3 }$
D) $10 ^ { 8 } \mathrm {~m} ^ { 3 }$
E) $10 ^ { 10 } \mathrm {~m} ^ { 3 }$

Question 58

Choose the one alternative that best completes the statement or answers the question.
A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A) $1333 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $250 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $750 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 59

Choose the one alternative that best completes the statement or answers the question.
A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight.

A) 5200 N
B) 520 N
C) 2600 N
D) 260 N

Question 60

Choose the one alternative that best completes the statement or answers the question.
A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of $2.0 \mathrm {~cm} ^ { 2 }$ If the large piston has an area of $40 \mathrm {~cm} ^ { 2 }$ how much weight can the large piston support? Assume the pistons each have negligible weight.

A) 10000 N
B) 40000 N
C) 500 N
D) 25 N

Question 61

Choose the one alternative that best completes the statement or answers the question.
Fluid flows at 2.0 m/s through a pipe of diameter 3.0 cm. What is the volume flow rate of the fluid?

A) $5.7 \times 10 - 3 \mathrm {~m} 3 / \mathrm { s }$
B) $57 \mathrm {~m} 3 / \mathrm { s }$
C) $14 \mathrm {~m} ^ { 3 / \mathrm { s } }$
D) $1.4 \times 10^ {- 3} \mathrm {~m}^ 3 / \mathrm { s }$

Question 62

Choose the one alternative that best completes the statement or answers the question.
Water, which we can treat as ideal and incompressible, flows at 12 m/s in a horizontal pipe with a pressure of $3.0 \times 10 ^ { 4 } \mathrm {~Pa}$
If the pipe widens to twice its original radius, what is the pressure in the wider section?

A) $9.8 \times 10 ^ { 4 } \mathrm {~Pa}$
B) $4.9 \times 10 ^ { 4 } \mathrm {~Pa}$
C) $7.4 \times 10 ^ { 4 } \mathrm {~Pa}$
D) $3.0 \times 10 ^ { 4 } \mathrm {~Pa}$

Question 63

Write the word or phrase that best completes each statement or answers the question.
A wooden raft has a mass of 55 kg. When empty it floats in water $\text { (density } 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \text { ) }$ with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

Question 64

Choose the one alternative that best completes the statement or answers the question.
A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

A) $960 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $56.1 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $1050 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $1040 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $1030 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s . What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

A) 5.1 m/s
B) 2.6 m/s
C) 0.32 m/s
D) 0.64 m/s
E) 1.3 m/s

Question 66

Choose the one alternative that best completes the statement or answers the question.
A pump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe. What is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? Treat the fluid as ideal and incompressible.

A) 6.0 cm/s
B) 50 cm/s
C) 22 cm/s
D) 51 cm/s

Question 67

Choose the one alternative that best completes the statement or answers the question.
Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 32m/s, what is its speed in this smaller section if the water behaves like an ideal incompressible fluid?

A) 43 m/s
B) 28 m/s
C) 37 m/s
D) 24 m/s

Question 68

Choose the one alternative that best completes the statement or answers the question.
A cylinder, semicircular in cross-section, is 10 m long and 5.0 m in radius. It is completely submerged, with its flat bottom side horizontal and 8.0 m below the water surface, as shown in the figure. What is the magnitude of the net force on the curved upper surface of the half-cylinder? Neglect atmospheric pressure.

A) $2.0 \times 10 ^ { 6 } \mathrm {~N}$
B) $3.0 \times 10 ^ { 6 } \mathrm {~N}$
C) $4.0 \times 10 ^ { 6 } \mathrm {~N}$
D) $3.5 \times 10 ^ { 6 } \mathrm {~N}$
E) $2.5 \times 10 ^ { 6 } \mathrm {~N}$

Question 69

Choose the one alternative that best completes the statement or answers the question.
A solid sphere of mass 8.6 kg, made of metal whose density is $3400 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values?

A) $1900 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $1400 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $1600 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $1700 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $1500 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question 70

Choose the one alternative that best completes the statement or answers the question.
The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of $880 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ to make it buoyant. If it is totally submerged in seawater with a density of $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and neither rising nor sinking, what is the weight of the Trieste craft?

A) 227 kN
B) 527 kN
C) 127 kN
D) 327 kN
E) 427 kN

Question 71

Choose the one alternative that best completes the statement or answers the question.
A rectangular wooden block measures $10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}$
When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is $1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

A) $1.65 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
B) $0.350 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
C) $0.825 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
D) $1.21 \mathrm {~g} / \mathrm { cm } ^ { 3 }$
E) $0.606 \mathrm { a } / \mathrm { cm } ^ { 3 }$

Question 72

Choose the one alternative that best completes the statement or answers the question.
Consider a very small hole in the bottom of a tank that is 17.0 cm in diameter and filled with water to a height of 90.0 cm. Find the speed at which the water exits the tank through the hole.

A) 44.1 m/s
B) 17.64 m/s
C) 48.3 m/s
D) 4.20 m/s

Question 73

Choose the one alternative that best completes the statement or answers the question.
A 4.7-kg solid sphere, made of metal whose density is $4000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ hangs by a light cord. When the sphere is immersed in water, what is the tension in the cord? The density of water is 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 } \text {. }$

A) 46 N
B) 58 N
C) 35 N
D) 52 N
E) 40 N

Question 74

Choose the one alternative that best completes the statement or answers the question.
A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? $\left( \rho \mathrm { Fe } = 7.87 \mathrm {~g} / \mathrm { cm } ^ { 3 } , \rho _ { \text {water } } = 1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$

A) 6.6 cm
B) 131 cm
C) 37 cm
D) 79 cm

Question 75

Choose the one alternative that best completes the statement or answers the question.
A hot air balloon along with its cargo has a mass of $4.0 \times 10 ^ { 5 } \mathrm {~kg}$ and it holds $7.0 \times 10 ^ { 5 } \mathrm {~m} ^ { 3 }$ of hot air. It is floating at a constant height in air with a density of $1.29 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
What is the density of the hot air in the balloon?

A) $0.57 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
B) $1.4 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
C) $0.86 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
D) $0.43 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
E) $0.72 \mathrm { kq } / \mathrm { m } ^ { 3 }$

Question 76

Choose the one alternative that best completes the statement or answers the question.
A barge is 10 m wide and 60 m long and has vertical sides. The bottom of the boat is 1.2 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } ?$

A) 6.8 MN
B) 6.4 MN
C) 7.1 MN
D) 3.5 MN
E) 9.5 MN

Question 77

Choose the one alternative that best completes the statement or answers the question.
Ideal incompressible fluid flows through a 4.0-cm-diameter pipe at 1.0 m/s . There is a 2.0 cm diameter constriction in the line. What is the speed of the fluid in this constriction?

A) 2.0 m/s
B) 0.50 m/s
C) 4.0 m/s
D) 0.25 m/s

Question 78

Choose the one alternative that best completes the statement or answers the question.
A hole of radius 1.0 mm forms in the bottom of a very large water storage tank that holds water to a depth of 15 m. At what volume rate will water flow out of the hole?

A) $5.4 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 } / \mathrm { s }$
B) $5.4 \times 10 ^ { - 6 } \mathrm {~m} ^ { 3 } / \mathrm { s }$
C) $5.4 \times 10 ^ { - 4 } \mathrm {~m} ^ { 3 } / \mathrm { s }$
D) $5.4 \times 10 ^ { - 7 } \mathrm {~m} ^ { 3 } / \mathrm { s }$

Question 79

Choose the one alternative that best completes the statement or answers the question.
A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ How much deeper into the water does the barge sink when $3.0 \times 10 ^ { 5 } \mathrm {~kg}$ of coal are Ioaded on the barge?

A) 1.0 m
B) 1.5 m
C) 50 cm
D) 75 cm
E) 25 cm

Question 80

Choose the one alternative that best completes the statement or answers the question.
A 200-kg flat-bottomed boat floats in fresh water, which has a density of $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
If the base of the boat is 1.42 m wide and 4.53 m long, to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is 257 kg?

A) 8.52 cm
B) 7.95 cm
C) 7.10 cm
D) 7.53 cm