# Measurement and Uncertainty Quiz

## Make sure to try these on a piece of paper first

Question #1-1 Paper 1 Difficulty: Easy

The radius of a sphere is r=12.37 m. What is the volume of the sphere correct to two significant figures?
A) $7928.62 \ \textrm{m}^{3}$
B) $7920 \ \textrm{m}^{3}$
C) $7928 \ \textrm{m}^{3}$
D) $7900 \ \textrm{m}^{3}$

Question #1-2 Paper 2 Difficulty: Medium

A ball is thrown in the air and 5 different students are individually measuring the time it takes to fall back down using stopwatches. The times obtained by each student are the following:
6.2 s, 6.0 s, 6.4 s, 6.1 s, 5.8 s

a) What is the uncertainty of the results?

b) How should the resulting time be expressed?

Question #1-3 Paper 2 Difficulty: Medium

A bullet travels a distance of $l=154\pm0.5$ m in the time $t=0.4\pm0.05$ s.

a) Calculate the fractional uncertainty for the speed of the bullet.

b) Calculate the percentage uncertainty for the speed of the bullet.

c) Write down the speed of the bullet using the absolute uncertainty.

Question #1-4 Paper 1 Difficulty: Medium

The volume of a pyramid with base length l, base width w, and height h is given by $V=\frac{lwh}{3}$. The volume of the pyramid was measured with an uncertainty of 12%, while the base length and base width were measured with an uncertainty of 4%. What is the uncertainty of the height of the pyramid?
A) 2%
B) 3%
C) 4%
D) 6%

Question #1-5 Paper 2 Difficulty: Medium

The current passing through a resistor is $I=3\pm0.1\ \textrm A$ and the resistance of the resistor is $R=13\pm0.5\ \Omega$. The electrical power, measured in watt (W), supplied to the resistor is given by $P=RI^{2}$.

a) Write down the value of the supplied power correct to one significant figure.

b) Find the percentage uncertainty for the current passing through the resistor and its resistance.

c) Find the absolute uncertainty for the electrical power.