Units and Conversion

The very first PhysicsBowl took place in 1985. Approximately how many seconds ago did students compete in this first contest?

(A) $10^{2}$
(B) $10^{5}$
(C) $10^{7}$
(D) $10^{9}$
(E) $10^{12}$

Which of the following is NOT a vector quantity?

(A) Acceleration
(B) Average Velocity
(C) Linear Momentum
(D) Potential Energy
(E) Force

Which of the following relationships correctly ranks the three given speeds from least to greatest? The speeds are given as $v_{1}=1.25\times 10^{-4}cm/\mu s, v_{2}=0.076Mm/week$ and $v_{3}=9.50km/day.$

(A) $v_{1}<v_{2}<v_{3}$
(B) $v_{3}<v_{2}<v_{1}$
(C) $v_{2}<v_{3}<v_{1}$
(D) $v_{1}<v_{3}<v_{2}$
(E) $v_{3}<v_{2}=v_{1}$

When computed with proper MKS units, the Universal Gas Constant divided by Boltzmann's constant is equal to

(A) the speed of light.
(B) Planck's constant.
(C) Avogadro's number.
(D) the permittivity of free space.
(E) the Universal Gravitational constant.

In terms of the seven fundamental SI units in the MKS system, the unit for capacitance is written as which of the following?

(A) $\displaystyle \frac{A^{2}}{kg\cdot m^{2}}$
(B) $\displaystyle \frac{A.\cdot s}{kgm^{2}}$
(C) $\displaystyle \frac{A\cdot s^{2}}{kg\cdot m}$
(D) $\displaystyle \frac{A^{2}.\cdot s^{3}}{kgm^{2}}$
(E) $\displaystyle \frac{A^{2}.\cdot s^{4}}{kgm^{2}}$

Which one of the following choices best represents the average mass of an adult human male?

(A) $1.0\times 10^{-2}kg$
(B) 1. $0\times 10^{-1}kg$
(C) 1. $0\times 10^{1}kg$
(D) 1. $0\times 10^{2}kg$
(E) 1. $0\times 10^{3}kg$

Albert Einstein's most famous equation is $E=mc^{2}$. The unit for the quantity represented by $E$ can be written as which one of the following options?

(A) seconds
(B) newtons
(C) kilograms
(D) meters
(E) joules

The distance of one thousand meters can be written as one kilometer. Which one of the following choices best represents a distance of one million meters?

(A) one gigameter
(B) one megameter
(C) one micrometer
(D) one nanometer
(E) one terameter

Which one of the following choices best represents the speed of 60. $0\displaystyle \frac{miles}{hr}$ rewritten in units of $\displaystyle \frac{km}{day}$ ?

(A) 2300
(B) 1440
(C) 900
(D) 4.00
(E) 1.56

Which one of the following is NOT a vector quantity?

(A) Linear momentum
(B) Electric field
(C) Average velocity
(D) Instantaneous acceleration
(E) Kinetic energy

The product $(3$Teslas)$\times(2$meters)$\times$( $4$ meters/second) is equivalent to which one of the following?

(A) 24 Amperes
(B) 24 Coulombs
(C) 24 Watts
(D) 24 Ohms
(E) 24 Volts

Which one of the following lengths is the largest?

(A) one centimeter
(B) one kilometer
(C) one millimeter

(D) one meter
(E) one nanometer

Which one of the following choices best represents the value of the speed of light using units of $\displaystyle \frac{miles}{week}$ ?

(A) $5.90\times 10^{12}$
(B) $1.13\times 10^{11}$
(C)$1.61\times 10^{10}$
(D) $6.75\times 10^{8}$
(E) $1.13\times 10^{8}$

Which one of the following quantities is a scalar quantity?

(A) Impulse
(B) Linear Momentum
(C) Acceleration
(D) Speed
(E) Displacement

The cylindrical head of an aluminum nail has a diameter of l.00 cm. For the top layer of atoms in the nail's head, which one of the following choices best represents the number of aluminum atoms in that layer?

(A) $10^{10}$
(B) $10^{15}$
(C) $10^{20}$
(D) $10^{25}$
(E) $10^{30}$

Red light from a laser is noted to have a wavelength of 632.8 nanometers. Which one of the following choices best represents the meaning of the prefix nano?

(A) $1\times 10^{-3}$
(B) $1\times 10^{-6}$
(C) $1\times 10^{-9}$
(D) $1\times 10^{-12}$
(E) $1\times 10^{-15}$

A scientist calculated a quantity that was equal to one light-year. Which one of the following choices represents the type of quantity that the scientist calculated?

(A) Time
(B) Mass
(C) Speed
(D) Force
(E) Distance

Which one of the following choices represents the base MKS units for sound intensity?

(A)$\frac{kg}{s^{3}}$
(B)$\frac{m}{kg\cdot s^{3}} $
(C)$\frac{m^{2}}{kg\cdot s^{2}}$
(D)$\frac{kg}{m\cdot s^{2}} $
(E)$\frac{s^{2}}{m\cdot kg}$

An FM radio station sends a signal with a frequency of 99. $99\times 10^{6}Hz$. Which one ofthe following choices best represents this frequency expressed using metric prefixes?

(A) 99.99 kHz
(B) 99.99 MHz
(C) 99.99 GHz
(D) 99.99 THz
(E) 99.99 nHz

Which one of the following quantities is not a scalar quantity?

(A) Force
(B) Energy
(C) Mass
(D) Speed
(E) Pressure

A rectangular block of wood has a mass of17.8 $g$ and dimensions of length: 3.00 cm, width: 4.00 cm, and height: 2.00 cm. Which one of the following choices correctly gives the average density of the block?

(A) $7.42\displaystyle \times 10^{5}\frac{kg}{m^{3}}$
(B) $7.42\displaystyle \times 10^{2}\frac{kg}{m^{3}}$
(C) $7.42\displaystyle \frac{kg}{m^{3}}$

(D) $7.42\displaystyle \times 10^{-1}\frac{kg}{m^{3}}$
(E) $7.42\displaystyle \times 10^{-4}\frac{kg}{m^{3}}$

Which one of the following choices correctly represents a length of 3.00 mm?

(A) $3.00\times 10^{-6}m$
(B) $3.00\times 10^{-3}m$
(C) $3.00\times 10^{-2}m$
(D) $3.00\times 10^{3}m$
(E) $3.00\times 10^{6}m$

Which one of the following quantities is not a vector quantity?

(A) Average speed
(B) Average velocity
(C) Linear momentum

(D) Acceleration
(E) Average force

A car travels at $20.0\displaystyle \frac{miles}{hr}$. Which one of the following choices best represents the speed of the car in SI units of $\displaystyle \frac{m}{s}$ ?

(A) $533\displaystyle \frac{m}{s}$
(B) $45.0\displaystyle \frac{m}{s}$
(C) 20. $0\displaystyle \frac{m}{s}$
(D) 8. $9\displaystyle \frac{m}{s}$
(E) 0. $75\displaystyle \frac{m}{s}$

Approximately how many hydrogen atoms are there in the liquid water of Earth's oceans?

(A) $10^{62}$
(B) $10^{57}$
(C) $10^{52}$
(D) $10^{47}$
(E) $10^{42}$

Which one of the following choices represents the base SI units of inductance?

(A) $\displaystyle \frac{kgm^{2}}{A^{2}s^{2}}$
(B) $\displaystyle \frac{kgm^{2}}{As}$
(C) $\displaystyle \frac{kgm}{A^{2}s^{2}}$
(D) $\displaystyle \frac{kgm^{2}}{A^{2}s^{3}}$
(E) $\displaystyle \frac{kgm}{A^{2}s^{3}}$

Which one of the following choices represents the smallest amount of time?

(A) 1 day
(B) 1 minute
(C) 1 second
(D) 1 week
(E) 1 year

A scientist obtains an answer that has units equivalent to those from computing the square root of the ratio of the Universal Gravitational constant to Coulomb's constant. Which one of the following choices has these same units?

(A) energy divided by time
(B) length divided by time
(C) mass divided by energy
(D) electric field strength divided by magnetic field strength
(E) charge divided by mass

A scientist computes a speed as $\displaystyle \frac{12mm}{3\mu s}$. Which one of the following choices represents this same speed?

(A) $4\displaystyle \frac{km}{s}$
(B) $4\displaystyle \frac{nm}{s}$
(C) $4\displaystyle \frac{m}{s}$
(D) $4\displaystyle \frac{Gm}{s}$
(E) $4\displaystyle \frac{pm}{s}$

Which one of the following choices is a vector quantity?

(A) average speed
(B) kinetic energy
(C) mass
(D) time
(E) acceleration

A shipment of parts is labeled in units of ohm.second." Which one of the following choices represents an equivalent unit?

(A) henry
(B) farad
(C)joule
(D) volt
(E) weber

A quick Google search reveals that your phone operates at a frequency of 850 $\mathrm{x}10^{6}$ Hz. Which of the following choices best represents this frequency using metric prefixes?

(A) 850 $\mu \mathrm{H}\mathrm{z}$
(B) 850 $\mathrm{m}\mathrm{H}\mathrm{z}$
(C) 850 $\mathrm{k}\mathrm{H}\mathrm{z}$
(D) 850 MHz
(E) 850 GHz

Which of the following is NOT a vector quantity?

(A) Acceleration
(B) Average velocity
(C) Linear momentum

(D) Potential energy
(E) Force

The mean diameter of the Earth is 12.76 $\mathrm{x}10^{3}$ km. What is the surface area of the Earth in $\mathrm{m}^{2}$?

(A) 4.01 $\mathrm{x}10^{7}$
(B) 5.12 $\mathrm{x}10^{14}$
(C) 1.09 $\mathrm{x}10^{21}$
(D) 1.68 $\mathrm{x}10^{9}$
(E) 2.05 $\mathrm{x}10^{15}$

A thick-walled metal pipe of length 20.0 cm has an inside diameter of 2.00 cm and an outside diameter of 2.40 cm. What is the total surface area of the pipe, including the inside, outside, and ends, in $\mathrm{c}\mathrm{m}^{2}$?

(A) 276
(B) 277
(C) 278
(D) 279
(E) 282

A radian per second is a unit of:

(A) angular displacement

(B) angular velocity

(C) angular acceleration

(D) angular momentum

(E) rotational kinetic energy

Select the smallest value from the choices below

(A) 15 $\mathrm{x}10^{-3}$
(B) 0.15 $\mathrm{x}10^{0}$
(C) 0.00015 $\mathrm{x}10^{3}$
(D) 150 $\mathrm{x}10^{-3}$
(E) 0.00000015 $\mathrm{x}10^{6}$

Which one of the following is not equivalent to 2.50 miles?

$(1.00\ \mathrm{m}\mathrm{i}\ =1.61\ \mathrm{k}\mathrm{m}\ =5280\ \mathrm{f}\mathrm{t},\ 1.00\ \mathrm{y}\mathrm{d}\ =3.00\ \mathrm{f}\mathrm{t}\ =12.0\ \mathrm{i}\mathrm{n}.)$

(A) 1.32 $\mathrm{x}10^{4}$ ft
(B) 1.58 $\mathrm{x}10^{5}$ in
(C) 4.02 $\mathrm{x}10^{3}$ km

(D) 4.40 $\mathrm{x}10^{3}$ yd
(E) 4.02 $\mathrm{x}10^{5}$ cm

The unit that is used to measure magnetic flux is:

(A) Coulomb
(B) Farad (F)
(C) Tesla (T)
(D) Weber (Wb)
(E) Henry (H)

The Joule (J) is a derived unit of energy in the International System of Units. It is equal to which of the following
(A) $\mathrm{kg}\left(\frac{\mathrm{m}}{\mathrm{s}}\right)$
(B) $\mathrm{kg}\left(\frac{\mathrm{m}}{\mathrm{s}^{2}}\right)$
(C) $\mathrm{kg}\left(\frac{m^{2}}{s}\right)$
(D) $\mathrm{kg}\left(\frac{\mathrm{m}^{2}}{\mathrm{~s}^{2}}\right)$
(E) $\operatorname{kg}\left(\frac{m^{2}}{s^{3}}\right)$

The average density of blood is $1.06 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Imagine that you donate a pint of blood during a local blood drive. What mass of blood, in grams, have you donated? ( $1 \mathrm{pt}=1 / 2 \mathrm{~L}$, $1 \mathrm{~L}=1000 \mathrm{~cm}^{3}$.)
(A) 530 g
(B) 0.530 g
(C) 5300 g
(D) $5.30 \times 10^{5} \mathrm{~g}$
(E) 53.0 g

A car engine moves a piston with a circular cross-section of 7.500 cm in diameter a distance of 3.250 cm to compress the gas in the cylinder. By what amount is the gas decreased in volume?
(A) $143.6 \mathrm{~cm}^{3}$
(B) $153.6 \mathrm{~cm}^{3}$
(C) $662.7 \mathrm{~cm}^{3}$
(D) $682.7 \mathrm{~cm}^{3}$
(E) $88.36 \mathrm{~cm}^{3}$

All of the following are base units of the SI system except:
(A) kilogram
(B) kelvin
(C) meter
(D) volt
(E) candela

There are $6.02 \times 10^{23}$ carbon atoms (Avogadro's number) in 12.0 g of carbon. If you could count one atom each second, how much time would it take to count the atoms in 1.0 g of carbon?
(A) $1.59 \times 10^{15}$ days
(B) $1.59 \times 10^{15}$ weeks
(C) $1.59 \times 10^{15}$ years
(D) $1.59 \times 10^{18}$ weeks
(E) $1.59 \times 10^{18}$ years

On November 16, 2022, the Artemis 1 rocket lifted off from Launch Pad 39 at Cape Canaveral, FL for its trip to the moon. To lift off, the engines supplied 8.8 million pounds $\left(4.0 \times 10^{7} \mathrm{~N}\right)$ of thrust. Which of the following does NOT express this thrust force?
(A) $4.0 \times 10^{10} \mathrm{mN}$
(B) $4.0 \times 10^{4} \mathrm{kN}$
(C) $4.0 \times 10^{1} \mathrm{MN}$
(D) $4.0 \times 10^{-3} \mathrm{GN}$
(E) $4.0 \times 10^{-5} \mathrm{TN}$

What is the conversion factor between $\mathrm{km} / \mathrm{hr}^{2}$ and $\mathrm{m} / \mathrm{s}^{2}$ ?
(A) $7.72 \times 10^{-6}$
(B) $7.72 \times 10^{-5}$
(C) 0.278
(D) $2.78 \times 10^{-2}$
(E) $2.78 \times 10^{-4}$

The radius of the Earth is 3963 miles. What is the surface area of the Earth in square meters?
(A) $4.9 \times 10^{7} \mathrm{~m}^{2}$
(B) $2.6 \times 10^{7} \mathrm{~m}^{2}$
(C) $1.3 \times 10^{14} \mathrm{~m}^{2}$
(D) $2.6 \times 10^{14} \mathrm{~m}^{2}$
(E) $5.1 \times 10^{14} \mathrm{~m}^{2}$

A researcher is measuring the average speed of a moving object over a known distance. The distance, $\mathrm{d}=5.0 \mathrm{~m}$, is measured with an uncertainty of $\pm 0.1 \mathrm{~m}$, and the time $\mathrm{t}=1.00 \mathrm{~s}$ is measured with an uncertainty of $\pm 0.02 \mathrm{~s}$. All uncertainties are independent and random. What is the uncertainty in measured average speed?
(A) $\pm 0.04 \mathrm{~m} / \mathrm{s}$
(B) $\pm 0.08 \mathrm{~m} / \mathrm{s}$
(C) $\pm 0.12 \mathrm{~m} / \mathrm{s}$
(D) $\pm 0.14 \mathrm{~m} / \mathrm{s}$
(E) $\pm 0.18 \mathrm{~m} / \mathrm{s}$