Black Hole

Basic

Moderate

Challenging

Difficult

Black Hole

Question 1 

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

Question 2 

The radius of a spherical planet is X and the absolute uncertainty in the radius of the planet is \Delta X. What is the fractional uncertainty in the volume of the planet?

1. \frac{4\pi}{3} \left (\frac{\Delta X}{X}  \right )^3
2. 4\pi \left (\frac{\Delta X}{X}  \right )
3. \left (\frac{\Delta X}{X}  \right )^3
4. 3 \left (\frac{\Delta X}{X}  \right )

Question 3 

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}

Question 4 

A student carries out an experiment to determine the speed of a toy car. The results of the experiment are shown on the graph. 

What is true about the random and the systematic errors in the student’s data?

Question 5 

The mass of a car is 1000 kg\pm5% It is moving at a constant speed of 30.0 m s^{-1}\pm3%. What is the percentage uncertainty in the kinetic energy of the car?

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

Question 6 

The side length of a cube is 20 \pm 5 cm. What is the absolute uncertainty in the volume of the cube?

1. 125 cm^{3}
2. 625 cm^{3}
3. 6000 cm^{3}
4. 8000 cm^{3}

Question 7 

A student measures the base of a triangle as 20 \pm 1 cm and its height as 8 cm \pm 4 %. What is the fractional uncertainty in the area of the triangle?

1. \frac{1}{20}
2. \frac{9}{100}
3. \frac{51}{100}
4. \frac{11}{20}

Question 8 

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%

Question 9 

A point charge is placed in an electric field. The uncertainty in the electric force that acts on the point charge is 8 % and the uncertainty in the charge of the point charge is 4 %.  What is the percentage uncertainty in the electric field strength?

1. 2 %
2. 4 %
3. 12 %
4. 32 %

Question 10 

The side length of a cube is 50 \pm 1 cm and its mass is 60 \pm 3 kg. What is the percentage uncertainty in the density of the cube?

1. 4 %
2. 7 %
3. 11 %
4. 13 %

Question 11 

The radius of a sphere is measured to be 10 \pm 1 cm. What is the best estimate for the absolute uncertainty in the volume of the sphere?

1. 1 cm^3
2. 12 cm^3
3. 100 cm^3
4. 1200 cm^3

Question 12 

Two masses, X and Y, are 62\pm2 kg and 28\pm1 kg respectively. Which of the following has the largest fractional uncertainty?

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

Question 13 

The period of a mass-spring system that oscillates with simple harmonic motion (SHM) can be calculated using the formula T = 2 \pi \sqrt{\frac{m}{k}} where T is the period of the oscillations, m is mass and k is the spring constant. The percentage uncertainty in the period is 4 % and the percentage uncertainty in the mass is 8 %. What is the percentage uncertainty in the spring constant?  

1. 0.5 %
2. 1 %
3. 16 %
4. 24 %

Question 14 

The graph shows a data set from an experiment. 

What is the percentage uncertainty in the vertical axis intercept of the line of best fit for the data set?

1. 30 %
2. 50 %
3. 70 %
4. 100 %

Question 15 

The mass of a car is 1000 kg \pm 5 % and its kinetic energy is 200 kJ \pm 15 %. What is the absolute uncertainty in the speed of the car?

1. 0.6 m s^{-1}
2. 1 m s^{-1}
3. 2 m s^{-1}
4. 4 m s^{-1}

Question 16 

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?

Question 17 

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}

Question 18 

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

Question 19 

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

Question 20 

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 betweenx and y?

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

Question 21 

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