Mass, Weight & Density (Cambridge (CIE) IGCSE Combined Science: Physics): Exam Questions

A ball made of poly(ethene) has a density of 0.9 g/cm³.

Predict what happens to the ball when placed in a beaker of water and in a beaker of ethanol.

Use the data in Table 9.1 to explain your answer.

water: ..................

ethanol: ..................

explanation: ..................

A thin, flat piece of aluminium is used as a mirror.

(i) The piece of aluminium has a mass of 9.0 g.

Use information from Table 9.1 to calculate the volume of the piece of aluminium.

[2]

(ii) Fig. 9.2 shows a person’s eye looking at the reflection of an object placed in front of the aluminium mirror.

Fig. 9.2

On Fig. 9.2:

• draw the normal line and label the angle of incidence of the incident ray with the letter i.

• draw the reflected ray to show how the eye is able to see the reflected image of the object.

[2]

You are going to determine the density of the material used to make a metre rule.

Fig. 4.1 shows the length L, width w and thickness t of a metre rule.

Fig. 4.1 (not to scale)

(i) Use the ruler to measure the width w and thickness t of your metre rule.

Record each measurement to the nearest $0.1\text{ cm}$.

[2]

(ii) The measurements in (a)(i) are recorded to the nearest $0.1\text{ cm}$.

State why it is not appropriate to record the measurements to the nearest $0.01\text{ cm}$.

[1]

(iii) The length L of the metre rule is $100.0\text{ cm}$.

Calculate the volume V of the metre rule.

Use your answers to (a)(i) and the equation shown.

$V=L\times w\times t$

[1]

You are going to determine the mass M of the metre rule using a balancing method.

(i) Procedure

step 1 Place the pivot directly under the 60 cm mark on the metre rule.

Fig. 4.2 shows distance d = 60.0 cm.

Fig. 4.2

step 2 Place the load on the metre rule.

step 3 Adjust the position of the load until the metre rule is as close to balance as possible.

Measure distance x₁ from the centre of the load to the pivot.

[1]

(ii) Procedure

step 4 Remove the load.

step 5 Move the pivot to directly underneath the 70 cm mark so that distance d = 70.0 cm.

step 6 Repeat step 2 and step 3 in (b)(i).

Measure distance X₂ from the centre of the load to the pivot.

[2]

(iii) Use your results for (b)(i) and (b)(ii) to calculate the mass M of the metre rule.

Use the equation shown.

M = 5 (x₁ + x₂)

[2]

(iv) State one practical difficulty involved in using this method to determine M.

[1]

Use your answers to (a)(iii) and (b)(iii) to calculate the density ρ of the material used to make the metre rule.

Use the equation shown.

$\rho =\frac{M}{V}$

Give your answer to two significant figures.

Give the unit for your answer.

A student determines the density of the material used to make a metre rule.

Fig. 4.1 shows the metre rule (not drawn to scale).

Fig. 4.1 (not to scale)

(i) On Fig. 4.1, draw a double-headed arrow (↔) to show the length L of the metre rule.

[1]

(ii) Fig. 4.2 shows the actual size of the end of the metre rule.

Fig. 4.2 (actual size)

Use a ruler to measure width w and thickness t of the metre rule in Fig. 4.2.

Record each measurement to the nearest 0.1 cm.

[2]

(iii) The measurements in (a)(ii) are recorded to the nearest 0.1 cm.

State why it is not appropriate to record the measurements to the nearest 0.01 cm.

[1]

(iv) The length L of the metre rule is 100.0 cm.

Calculate the volume V of the metre rule.

Use your answers to (a)(ii) and the equation shown.

$V=L\times w\times t$

[1]

The student determines the mass M of the metre rule using a balancing method.

Procedure

The student:

step 1 places a pivot directly under the 60.0 cm mark on the metre rule.

Fig. 4.3 shows the distance d = 60.0 cm.

Fig. 4.3 (not to scale)

step 2 places a load on the metre rule and adjusts the position of the load so that the rule balances

step 3 records that the centre of the load is directly above the 67.1 cm mark on the metre rule.

(i) Calculate the distance $x_1$ from the centre of the load to the pivot.

[1]

step 4 moves the pivot so that distance d = 70.0 cm

step 5 adjusts the position of the load so that the metre rule balances

step 6 records that the centre of the load is directly above the 84.2 cm mark on the metre rule

(ii) Calculate the distance $x_2$ from the centre of the load to the pivot.

[1]

(iii) Use the results for (b)(i) and (b)(ii) to calculate the mass M of the metre rule.

Use the equation shown.

$M=5(x_1+x_2)$

[1]

Fig. 4.4 shows apparatus used for measuring mass.

Fig. 4.4

(i) State the name of the apparatus shown in Fig. 4.4.

[1]

(ii) The apparatus in Fig. 4.4 is showing an error.

State the type of error shown in Fig. 4.4.

[1]

Use your answers to (a)(iv) and (b)(iii) to calculate the density ρ of the material used to make the metre rule.

Use the equation shown.

$\rho =\frac{M}{V}$

Give your answer to two significant figures.

Give the unit for your answer.