Measurements and Uncertainties

Which of the following is the correct multiplier for 'Tera'?

What is the SI unit for speed or velocity?

Which of the following is equivalent to $1\ mm^2$?

The symbol 'mol' refers to which physical quantity?

Which of the following expressions has the SI base unit $A \cdot s$?

In thermodynamics, the product of pressure ($P$) and volume ($V$) has the same units as which of the following?

The gradient of a displacement-time graph represents velocity. What is the SI base unit of this gradient?

Electric susceptibility is a dimensionless constant. It relates the polarization $P$ (dipole moment per unit volume) to the electric field $E$. What are the SI base units of polarization $P$?

What is the SI base unit for the expression $\frac{h}{mc}$, where $h$ is Planck's constant, $m$ is mass, and $c$ is the speed of light?

In the equation for the speed of sound in a gas, $v = \sqrt{\frac{\gamma P}{\rho}}$, $\gamma$ is a dimensionless constant. What are the SI base units of the ratio $\frac{P}{\rho}$?

In the context of the IB Physics syllabus, 'uncertainty' is a measure of:

If a student wants to reduce the impact of their personal reaction time in a timing experiment, they should:

A systematic error is also sometimes referred to as:

A student measures the speed of sound and gets $330\text{ m s}^{-1}$, $332\text{ m s}^{-1}$, and $328\text{ m s}^{-1}$. The accepted value is $343\text{ m s}^{-1}$. The student's results are:

When reading a scale on a ruler, a student always aligns the end of the object with the $1\text{ cm}$ mark instead of the zero mark and then subtracts $1\text{ cm}$ from the final reading. This technique is used to:

A rectangular plate has length $L \pm \Delta L$ and width $W \pm \Delta W$. The uncertainty in its area $A$ is $\Delta A$. Which expression for the fractional uncertainty in $A$ is correct?

A student measures the mass of several identical coins together and then divides by the number of coins. This procedure is done to:

In an experiment to measure the speed of light using a rotating mirror, if the angular velocity of the mirror is consistently $1\%$ lower than the frequency counter indicates, the resulting value for the speed of light will be:

If the formula for kinetic energy is $E_k = \frac{1}{2}mv^2$, and $v$ is measured with an ammeter and voltmeter in a circuit where $v$ is proportional to current ($v = kI$), a $5\%$ systematic error in the current measurement will lead to what percentage error in the calculated kinetic energy?

A scientist finds that a certain measurement follows a Gaussian (normal) distribution. If the scientist increases the number of trials from 10 to 1000, which of the following will significantly decrease?

An object moves along a semi-circular path from point $X$ to point $Y$. If the radius of the semi-circle is $R$, what is the magnitude of the displacement of the object?

Which of the following mathematical operations is considered invalid when combining a scalar quantity $k$ and a vector quantity $\vec{V}$?

In a scale diagram representing a vector quantity, what property of the physical quantity is primarily indicated by the orientation and the arrowhead of the drawn line?

Which list contains only scalar quantities?

An object is acted upon by two perpendicular forces, $F_x$ (horizontal) and $F_y$ (vertical). The magnitude of the horizontal force $F_x$ is $12.0\text{ N}$. The resultant force $F_{total}$ acting on the object is found to have a magnitude of $13.0\text{ N}$. What is the magnitude of the vertical force $F_y$?

A car is initially traveling due East with a constant speed $v$. The driver then turns the car so that it travels due North with the same speed $v$. Which of the following best describes the change in velocity vector $\Delta v$ of the car?

A ship moves at $20\text{ km h}^{-1}$ on a bearing of $090^\circ$. A current moves at $5\text{ km h}^{-1}$ on a bearing of $180^\circ$. What is the magnitude of the resultant velocity?

The scalar product $P$ of two vectors is given by the formula $P = AB \cos \theta$, where $A$ and $B$ are the magnitudes of the vectors and $\theta$ is the angle between them. A student measures these values as:

$A = (10.0 \pm 0.5) \text{ m}$ $B = (20.0 \pm 1.0) \text{ m}$ $\theta = (60.0 \pm 2.0)^{\circ}$

Which of the following is the best estimate for the absolute uncertainty in the calculated value of $P$? (Use $\pi \approx 3.14$, $\sin 60^{\circ} \approx 0.87$, and $\cos 60^{\circ} = 0.50$)

What is the minimum number of non-coplanar vectors required to have a zero resultant?

A vector $\vec{A}$ has a magnitude of $6 \text{ units}$ and vector $\vec{B}$ has a magnitude of $8 \text{ units}$. If the magnitude of the resultant is $10 \text{ units}$, what is the scalar product $\vec{A} \cdot \vec{B}$?

If $p = m / q$, and $m$ has a $3\%$ uncertainty while $q$ has a $2\%$ uncertainty, the uncertainty in $p$ is:

The side of a cube is $10.0 \pm 0.2$ cm. What is the percentage uncertainty in the volume of the cube?

The uncertainty in a measurement $1.00 \pm 0.01$ is $1\%$. What is the uncertainty in the square of this measurement?

A student measures a time interval as $\Delta t = 20.0 \pm 0.4$ s. What is the percentage uncertainty?

A voltage is measured as $V = 100 \pm 2$ V. What is the percentage uncertainty in $V^3$?

A student measures the time for 20 oscillations of a pendulum as $t = 30.0 \pm 0.2$ s. What is the absolute uncertainty in the time for a single oscillation $T = \frac{t}{20}$?

The centripetal force is $F = \frac{mv^2}{r}$. If $m$ has $1\%$ uncertainty, $v$ has $2\%$ uncertainty, and $r$ has $3\%$ uncertainty, what is the percentage uncertainty in $F$?

The value of a quantity is $X = \frac{A-B}{C}$. Given $A = 20 \pm 1$, $B = 10 \pm 1$, and $C = 5 \pm 0.5$. What is the absolute uncertainty in $X$?

Which of the following would result in the largest percentage uncertainty in the calculated value of kinetic energy $E_k = \frac{1}{2}mv^2$?

A student determines the density of a liquid using $\rho = \frac{m}{V}$. The mass of the empty beaker is $50 \pm 1$ g and the mass of the beaker with liquid is $150 \pm 1$ g. The volume of liquid is $100 \pm 2$ mL. What is the percentage uncertainty in $\rho$?