Physics 1.2 - Measurements And Uncertainties

1. Which of the following is SI base unit?

Degree Celsius

Ampere

Coulomb

Gram

Ampere is the SI base unit for current.

Degree Celsius is not temperature’s SI unit. It should be Kelvin. So A is wrong.

Coulomb is a derived SI unit. It is the unit of charge, which is equivalent to . So C is wrong

Gram is not the base unit. The base unit for mass is kilogram. So D is wrong

Year is not the base unit. The base unit for time is second. So E is wrong

Explanation

Ampere is the SI base unit for current.

Degree Celsius is not temperature’s SI unit. It should be Kelvin. So A is wrong.

Coulomb is a derived SI unit. It is the unit of charge, which is equivalent to . So C is wrong

Gram is not the base unit. The base unit for mass is kilogram. So D is wrong

Year is not the base unit. The base unit for time is second. So E is wrong

2. Which of the following is equivalent to the derives unit J? J is the unit of work.

Because we have work = force x distance = mass x acceleration x distance. Thus we have, considering an object of 1 kg get moved at for , then the work will equal to

work =

=

=

Explanation

Because we have work = force x distance = mass x acceleration x distance. Thus we have, considering an object of 1 kg get moved at for , then the work will equal to

work =

=

=

3. Which of the following measurements have three significant digits?

A table is reported to be 1.356 meters

A fly is measured to be 0.012 grams

An airplane is as heavy as 500 tons

A currant in a circuit is 20.0 mA

Because of the decimal point, the zeroes on the right of 2 of choice D do count. So D has 3 significant digits.

Choice A has 4 significant digits.
Choice B has 2 significant digits, because the zeroes on the left do not count
Choice C has 1 significant digit, because the zeroes on the right do not count without a decimal point.

Explanation

Because of the decimal point, the zeroes on the right of 2 of choice D do count. So D has 3 significant digits.

Choice A has 4 significant digits.
Choice B has 2 significant digits, because the zeroes on the left do not count
Choice C has 1 significant digit, because the zeroes on the right do not count without a decimal point.

4. The age of the universe is 14 billion years. How many seconds is 14 billion years closest to?

14 billions years years secs.

If 1 year is converted to seconds, you will get wrong answer A. If only billion years get converted to years, you will get the wrong answer B.

Explanation

14 billions years years secs.

If 1 year is converted to seconds, you will get wrong answer A. If only billion years get converted to years, you will get the wrong answer B.

5. All the following are all systematic errors except...?

The flow of air causing the reading of the temperature to change from time to time

A volumetric cylinder that is used to measure the volume of the liquid has a bump on the cylinder.

An ammeter shows a current of 0.1 A before we link it to the circuit.

A student uses a ruler and reads his measurement always on one side of the reading.

The air flow can decrease or increase the temperature reading, so it is a random error.

If a volumetric cylinder has a bump, then the liquid will be always more than the reading. So it is a systematic error.

If an ammeter has a zero error of 0.1 A, then the reading of the ammeter would be always more than the current in the circuit. So it is a systematic error.

If a student did not read the ruler with his eye directly above the ruler, he will always get a measurement smaller (standing on the left of the ruler), or bigger (standing on the right of the ruler). So it is a systematic error.

Explanation

The air flow can decrease or increase the temperature reading, so it is a random error.

If a volumetric cylinder has a bump, then the liquid will be always more than the reading. So it is a systematic error.

If an ammeter has a zero error of 0.1 A, then the reading of the ammeter would be always more than the current in the circuit. So it is a systematic error.

If a student did not read the ruler with his eye directly above the ruler, he will always get a measurement smaller (standing on the left of the ruler), or bigger (standing on the right of the ruler). So it is a systematic error.

6. If the diameter of an atom is about 100pm, what is diameter in terms of km?

100 pm= 100pm x

If you calculate 100 m in terms of km, then you will get wrong answer A. If you calculate 100 pm in terms of m, then you will get wrong answer C. If you calculate 1pm in terms of km, you will get wrong answer E.

Explanation

100 pm= 100pm x

If you calculate 100 m in terms of km, then you will get wrong answer A. If you calculate 100 pm in terms of m, then you will get wrong answer C. If you calculate 1pm in terms of km, you will get wrong answer E.

7. A chemist is pouring some solution from a volumetric cylinder to a tube to perform some experiment. Before he pours the solution, he finds the volume of the solution is

. After he pours the solution, he finds the volume of the solution is

. What is the volume of the solution he pours into the tube?

We calculate the measurement of the solution by subtracting the remaining solution from the original solution, so we have .

Even if we use subtraction to find the volume of the solution that is poured out, we will add the uncertainties. So the uncertainty of the volume of the solution is

But it does not make sense to record the measurement of the solution 5.2 mL if the uncertainty is 1 mL. So the volume of the solution is actually .

If you forget to add the uncertainty, you will get wrong answer A. If you subtract the uncertainty, you will get wrong answer D. If you did not change your measurement according to the new uncertainty, you will get wrong answer B.

Explanation

We calculate the measurement of the solution by subtracting the remaining solution from the original solution, so we have .

Even if we use subtraction to find the volume of the solution that is poured out, we will add the uncertainties. So the uncertainty of the volume of the solution is

But it does not make sense to record the measurement of the solution 5.2 mL if the uncertainty is 1 mL. So the volume of the solution is actually .

If you forget to add the uncertainty, you will get wrong answer A. If you subtract the uncertainty, you will get wrong answer D. If you did not change your measurement according to the new uncertainty, you will get wrong answer B.