Black Hole

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Moderate

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Black Hole

Question 1 

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 2 

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 3 

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 4 

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 5 

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 6 

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 7 

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 8 

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 9 

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 10 

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}