9702_m16_qp_52 Question 1

 

Defining the problem 

• k is the independent variable and h is the dependent variable 

• keep the mass of the object constant 

Methods of data collection

• Set-up the equipment as shown in the diagram.

• Fix a rod using a boss at the near top of a retort stand.

• Tie the elastic cord on the rod, The other end to be tied at the hook of the hanging mass.

• Fix a ruler with its 0 mark at the same level as the top fixed end of cord using clips or clamps. 

• Fix an electromagnet so that the end of the nail is at the same level as the fixed end of the cord and the 0 mark of ruler.This is needed to ensure that the starting point is the same throughout the experiment.

• Measure the mass m using a weighing scale. 

• To determine the spring constant k of each cord, 

• hang a few weights, one at a time, 

• determine the corresponding extensions by subtracting the original length L from the length after a weight is hanged, and

• plot a graph of weight against extension and determine the gradient

• The gradient is the k of a cord

• For each cord with its spring constant k already determined,

• tie the mass m previously selected, then measure the length L between the two ends

• release the mass m from the upper fixed end [the ruler’s 0 mark] of the cord  

• measure h or maximum distance fallen by the object using the ruler

Method of analysis 

•  Plot a graph of (h - L)2 / h against 1/ k 

•  To determine g

• calculate the gradient of the graph

• use this gradient to determine g

g = gradient / 2m  

•  The relationship is valid if the graph is 

• a straight line 

• passing through the origin.

Additional detail

• When releasing or dropping the mass, use safety goggles. Place a sand bag directly below the dropping so that it catches the mass m thereby protecting the investigator and the floor.

• Use cords that 

• are elastic but, with the assumed hanging mass m, will not hit the floor or the surface of the table where  the experiment is being done. Do trials first.

• obey Hooke’s Law, that is, with the hanging mass m chosen, it will not reach its elastic limit.

• The retort stand is usually vertical. In case unsure, check using a set square.

• For each cord, repeat the experiment several times, then determine the average h.

9702_s22_qp_22 Question 1

 

9702_s22_qp_12 Question 3

Which statement about systematic errors is not correct? 

A A systematic error can be caused by using an incorrectly calibrated instrument. 

B One particular type of systematic error can affect all the measurements by the same amount. 

C The effect of a systematic error can be reduced by repeating and averaging the measurements. 

D Zero error is a type of systematic error.

ANSWER: C

The Physics Behind

• Systematic error is an error associated with uncalibrated or faulty equipment or incorrect measurement practice which tend to affect all data in an investigation or experiment.
• Options A, B and C are all correct.

9702_s22_qp_12 Question 2

 What is the symbol for the SI base unit of temperature? 

A C 

B K 

C °C 

D °K

ANSWER: B

The Physics Behind

• C is the symbol used for coulomb, a unit of charge. So option A cannot be the answer.
• °C is a unit of temperature but not its SI unit. So option C is not the answer either.
• Temperature is a scalar quantity and in a sense must have a lowest possible value of zero unit just as other scalars like length, mass, time.... there are no negative magnitudes for these, the lowest magnitude is zero.
• In Celsius scale, Fahrenheit scale, Rankine scale, and others, the degree symbol in corresponding units °C, °F and °R implies a "degree" or a comparison. These scales can have "negative magnitude of a scalar".
• The SI unit of temperature is kelvin.
• Temperature expressed in kelvins is also called the absolute temperature or thermodynamic temperature.
• The lowest temperature in this scale is zero [absolute zero].
• The symbol is K and not °K in relation to explanation given in bullet 4 above.

9702_s22_qp_12 Question 1

Which estimate is reasonable? 

A 1 x 10^–3 kg for the mass of a grain of sand 

B 1 x 10^–2 m³ for the volume of a tennis ball 

C 1 x 10⁰ J for the work done lifting an apple from waist height to head height 

D 1 x 10⁴ W for the power of a light bulb in a house 

ANSWER: C

The Physics Behind

• Imagine normal apples being sold in stores. The masses differ between 70 and 200 grams [estimate].
• The corresponding weights therefore ranges from 0.7 N to 2 N.
• For the distance between the waist and head is about a little less than 1 metre.
• Option C therefore is reasonable.

9702_s22_qp_11 Question 3

 A value for the acceleration of free fall on Earth is given as (10  ± 2) m s^–2. 

Which statement is correct? 

A The value is accurate but not precise. 

B The value is both precise and accurate. 

C The value is neither precise nor accurate. 

D The value is precise but not accurate.

ANSWER: A

The Physics Behind 

• Accuracy is the term used to refer to how close a measurement is to the true or accepted value. 
• Precision refers to how close measurements of the same item are to each other. 
• By stating (10  ± 2) m s^–2, it means that 
• the acceleration, 10 m s^–2, is measured representing how close it is to the accepted value of g, and
• this acceleration can vary from 8.0 to 12 [± 2 m s^–2] implying closeness of measurements when experiment / method of determining g is repeated.
• The above implies accuracy and precision respectively. Thus, the answer is B.

9702_s22_qp_11 Question 2

Which two units are identical when expressed in terms of SI base units? 

A J C^–1 and kgm² A^–1s^–2 

B J s and kg m²s^–1

C N m and kgm³s^–2 

D Ns and kgm s^–3

ANSWER: B

The Physics Behind 

• The following are some SI derived units and where they are based from.
• 1 J = 1 Nm
• 1 N = 1 kg m s^–2
• Using the above,

1 J s = 1 Nm s

1 J s = 1 kg m s^–2 m s

1 J s = 1 kg m²s^–1

9702_s22_qp_11 Question 1

Which term represents a physical quantity? 

A metre 

B percentage uncertainty 

C quark flavour 

D spring constant 

ANSWER: D

The Physics Behind 

• Spring constant is the measured by dividing the restoring force [a physical quantity] by the extension of the spring [another physical quantity].
• Operating with these 2 physical quantities yields another physical quantity.

9702_s22_qp_13 Question 3

The drag coefficient C_d is a number with no units. It is used to compare the drag on different cars at different speeds. C_d is given by the equation

 Cd = 2F / vⁿρA 

where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the car and v is the speed of the car. 

What is the value of n? 

A 1 

B 2 

C 3 

D 4

ANSWER: B

The Physics behind the answer:

• The key idea here is to do dimensional analysis i.e. see what exponent n must be so that the units of 2F is the same as the unit of vⁿρA.
• For the 2F,
• the unit is N
• which is defined as kg m s^-2
• For the vⁿρA,
• the unit of v is (m s^-1)ⁿ, ρ is kg m^-3, and A is m²
• simplifying the above gives (m s^-1)ⁿ kg m^-1
• Combining the above 2 sets of units, we will have 
• the kgs cancel each other
• leading to m² s^-2 / (m s^-1)ⁿ 
• Now, it is clear that n = 2 for these 2 sets of units cancel each other i.e. to be unitless.

9702_s22_qp_13 Question 4

A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The measurement of the diameter is 5.00 mm ± 0.01 mm. 

What is the percentage uncertainty in the calculated volume of the sphere, using these values? 

A 0.2% 

B 0.4% 

C 0.6% 

D 1.2%

ANSWER: C

The Physics behind the answer:

• By volume, you should know that it considers 3 dimensions. This is implied in the formulas for volume, (4/3)πr3 where r is the radius for the sphere in particular.
• The uncertainty of a result of multiplication/division is the sum of percentage uncertainties of the dimensions [quantities] used in the calculations.
• Since you are given absolute uncertainty, this must be converted to percentage uncertainty first. The diameter 5.00 mm ± 0.01 mm is same as 5.00 mm ± 0.2%.
• Because radius [or half of diameter] is multiplied to itself a couple of times, then the uncertainty as explained above should be 0.2% + 0.2% + 0.2%.
•  The answer therefore is C, 0.6%.

9702_s22_qp_13 Question 2

Which list of unit prefixes decreases in magnitude from left to right? 

A centi, deci, milli 

B deci, milli, centi 

C pico, kilo, milli 

D kilo, milli, pico 

ANSWER: D

The Physics behind the answer:

• The options all have 3 prefixes with power of 10 magnitudes.
• However, the only option that has descending order of magnitudes is D.
• kilo means 10³
• milli means 10^-3
• pico means 10^-9

9702_s22_qp_13 Question 1

 Which pair of quantities are physical quantities? 

A charge and ampere 

B efficiency and kilogram 

C pascal and strain 

D period and potential difference

ANSWER: D

The Physics behind the answer:

• Physical quantities are those properties that we may be able to measure. A unit on the other hand is the one quantity where we compare any other quantities. 
• For example, saying that "my sister is 5 Physics books tall" you are describing a quantity i.e. height and comparing it with the unit Physics book. This is to say that if you know the length of a Physics book, then the height of the sister is 5 times of that. In everyday usage, however, we do not use the Physics book as a unit. Instead, we use a metre, centimetre, inches, feet, etc.. We say 5 metre or 5 cm or 5 feet, and others.
• You should see that units are written after the number describing a physical quantity. 
• Among the options, only D has both physical quantities - period and potential difference - of units second and volts, respectively.