# Physics HL

## Measurements and Uncertainties

Question difficulty level: Basic Moderate Challenging Difficult Black Hole Basic Moderate Challenging Difficult Black Hole

##### A bit more about difficulty levels (click)

Basic: Simple, usually one-step or definition-style questions to help you revise the basics.

Moderate: At the level of easier IB exam questions. Slightly more challenging than one-plane problems.

Difficult: This is how more challenging IB exam questions look like. If you can solve these with ease, you are in a good shape :)

Black Hole: Extra challenge for those with lightspeed thinking! Very few questions on your exam will be this difficult.

fas|fa-thumbs-up|

#### Tips on how to get the most out of the Questionbank

On Paper 1 questions, in addition to the correct answer (A, B, C or D), you will find:

A detailed, step-by-step Video Solution to help you fully understand the concepts used when solving the question.

• A lightning-quick Done Under 90 explanation with shortcuts, tips and tricks to help you save time on Paper 1, where, on average, you have 90 seconds per question.

• Purple text at the end of all videos to help you remember general concepts (Video Solutions) or to give you exam-taking tips to boost your grade (Done Under 90).

• The thumbnail of each video is set as the worked solution of the question to help you revise these solutions at a glance, without having to play each video individually.

## Paper 1

#### Question 1 The number of significant figures in $0.02670$ is:

1. 3
2. 4
3. 5
4. 6

B.

#### Question 2 Which of the following are two vector quantities?

1. Speed, Mass
2. Speed, Force
3. Velocity, Mass
4. Force, Velocity

D.

#### Question 3 Repeating readings in an experiment reduces:

1. Both random and systematic errors
2. Random errors only
3. Systematic errors only
4. Neither random, nor systematic errors

B.

#### Question 4 Which of the following are two fundamental SI units?

1. mole, kelvin
2. ampere, pascal
3. joule, meter
4. second, newton

A.

#### Question 5 A ball of $0.18$ kg is traveling at a speed of $3.210$ m s$^{-1}$. The mass and the velocity of the ball are used to calculate the magnitude of its momentum. What is the correct number of significant figures for the magnitude of the ball’s momentum?

1. 2
2. 3
3. 4
4. 5

A.

#### Question 6 What is the unit of pressure in fundamental SI units?

1. N m$^{-1}$
2. N m$^{-2}$
3. kg m$^{-1}$ s$^{-2}$
4. kg m$^{-2}$ s$^{-2}$

C.

#### Question 7 A particle is moving upwards in a straight line at constant speed. Which diagram represents the forces acting on this particle? D.

#### Question 8 Which of the following quantities has the fundamental SI unit combination of kg m s$^{-1}$?

1. Power
2. Energy
3. Impulse
4. Force

C.

#### Question 9 The side length of a square is measured to be $y \pm \Delta y$. What is the fractional uncertainty in the area of the square?

1. $\frac{\Delta y}{y}$
2. $\frac{2 \Delta y}{y}$
3. $\frac{\Delta y}{2y}$
4. $\left ( \frac{\Delta y}{y} \right )^{2}$

B.

#### Question 10 What is the order of magnitude, in cm, of an adult human being who has an average height?

1. $-1$
2. $0$
3. $1$
4. $2$

D.

#### Question 11 The mass of a car is 1000 kg$\pm$5% It is moving at a constant speed of 30.0 m s$^{-1}$$\pm$3%. What is the percentage uncertainty in the kinetic energy of the car?

1. 8 %
2. 11 %
3. 14 %
4. 45 %

B.

#### Question 12 Which of the following is a unit of acceleration?

1. J kg$^{-1}$ m$^{-1}$
2. N kg$^{-1}$ m$^{-1}$
3.  J kg m$^{-1}$
4. N kg m$^{-1}$

A.

#### Question 13 What is the size of a carbon nucleus?

1. 0.0027 fm
2. 0.0027 pm
3. 0.0027 nm
4. 0.0027 $\mu$m

B.

A.

#### Question 15 The mass of an object is $5.0 \pm 0.1$ kg and its speed is $20 \pm 1$ m s$^{-1}$.

What is the percentage uncertainty in the kinetic energy of the object?

1. $6$%
2. $7$%
3. $12$%
4. $25$%

C.

#### Question 16 Two masses, X and Y, are 62$\pm$2 kg and 28$\pm$1 kg respectively. Which of the following has the largest fractional uncertainty?

1. $2$X + Y
2. X – $2$Y
3. $\frac{3Y}{X}$
4. $4$XY

B.

#### Question 17 A coal-fired power plant uses $9 \times 10^{6}$ kg of coal per day. All the coal that is used in the power plant is composed of carbon-12 atoms.

What is the best estimate for the number of carbon-12 atoms used per month in the power plant?

1. $10^{9}$
2. $10^{24}$
3. $10^{31}$
4. $10^{34}$

D.

#### Question 18 A student carries out an experiment to examine how the kinetic energy of an object varies with the speed of the object. The results are shown on the graph. What can be deduced about the type of errors in the student’s measurements?

 Random errors Systematic errors A. Small Small B. Small Large C. Large Small D. Large Large

B.

#### Question 19 A stone is thrown with initial velocity $v$ at an angle $\theta$ to the horizontal. The magnitude of the vertical component of the stone’s velocity is $10$ m s$^{-1}$

What is the value of $\theta$?

1. sin$^{-1}\left ( \frac{10}{v} \right )$
2. sin$^{-1}\left ( \frac{v}{10} \right )$
3. cos$^{-1}\left ( \frac{10}{v} \right )$
4. cos$^{-1}\left ( \frac{v}{10} \right )$

A.

#### Question 20 A box is in the shape of a rectangular prism. The length, width and height of the box are measured to be $5$ cm, $10$ cm, and $20$ cm respectively. The uncertainty in each measurement is $\pm 1$ cm.

What is the absolute uncertainty in the volume of the box?

1. $3.5$ cm$^{3}$
2. $100$ cm$^{3}$
3. $350$ cm$^{3}$
4. $500$ cm$^{3}$

C.

#### Question 21 The volume of a cone is $30\pi \pm 0.9 \pi$ cm$^{3}$ and its height is $100 \pm 7$ mm. The volume of a cone can be calculated using $V = \frac{1}{3} \pi r^{2} h$ where V is volume, r is radius and h is height.

What is the absolute uncertainty in the diameter of the cone?

1. 0.01 m
2. 0.005 m
3. 0.003 m
4. 0.002 m

C.

#### Question 22 Three forces, $\overrightarrow{A}$, $\overrightarrow{B}$ and $\overrightarrow{C}$, act on object X as shown on the diagram. Object X moves at constant velocity. Consider the following three equations:

I. $\overrightarrow{A} + \overrightarrow{B} = - \overrightarrow{C}$

II. $\left | \overrightarrow{B} \right |$cos$(\alpha) = \left | \overrightarrow{C} \right |$cos$\left ( \frac{\pi}{2} - \alpha \right )$

III. $\left | \overrightarrow{A} \right | = \left | \overrightarrow{B} \right |$sin$(\alpha) + \left | \overrightarrow{C} \right |$cos$(\alpha)$

Which of these three equations are correct?

1. I and II only
2. I and III only
3. II and III only
4. I, II and III

D.

#### Question 23 A stone is attached to a metal rod and rotated in a horizontal circle. The centripetal acceleration, $a$, of the stone is measured for different rotational time periods, $T$

Given that random errors were minimised during the experiment, which of the following graphs will have a straight line of best fit?

1. $a$ against $T^{2}$
2. $a^{2}$ against $T$
3. $a$ against $T^{-2}$
4. $a^{-2}$ against $T$

C.

#### Question 24 Two quantities, $x$ and $y$, are related as shown on the graph. The vertical axis intercept of the graph is $c$ and the gradient of the graph is $\frac{1}{m}$. Which of the following equations correctly shows the relationship between$x$ and $y$?

1. $c = y - mx$
2. $c = my - x$
3. $x = my - c$
4. $x = my - mc$

D.

#### Question 25 In an experiment, the following values are measured and given together with their uncertainties:

$a = 2.0 \pm x$

$b = 16 \pm 2$%

$c = 0.50 \pm 0.07$

Then, $H$ is calculated using the formula $H = \frac{3a^{3}}{2 \sqrt{b} \times c}$. For the values given above, the absolute uncertainty in $H$ is $\pm 1.8$.

What is the value of $x$?

1. $0.1$
2. $0.2$
3. $0.3$
4. $0.4$