[Maximum number: 1]

Which row shows a base quantity with its correct SI unit?

quantity

unit

current

A

mass

g

temperature

${ }^{\circ} \mathrm{C}$

weight

N

[Maximum number: 1]

The rate of flow Q of a liquid along a narrow pipe of length L and radius r is given by

Q=\frac{\alpha r^{4}}{L}

where $\alpha$ is a constant.

An experiment is carried out to determine the value of $\alpha$ . The data from the experiment are shown in Table 1.1.

Table 1.1

(a)

Use information in Table 1.1 to show that the SI base unit of $\alpha$ is $\mathrm{s}^{-1}$ .

[ 1 ]

(a)

Underline all the SI base units in the following list.
ampere
coulomb
current
kelvin
newton

[ 1 ]

(a)

A horizontal pipe has length L and a circular cross-section of radius R. A liquid of density $\rho$ flows through the pipe. The mass m of liquid flowing through the pipe in time t is given by

m=\frac{\pi\left(p_{2}-p_{1}\right) R^{4} \rho t}{8 k L}

where $p_{1}$ and $p_{2}$ are the pressures at the ends of the pipe and k is a constant.
Determine the SI base units of k.

SI base units

[ 3 ]

(a)

The radius of a small sphere is determined from a measurement of the volume of the sphere. The sphere is submerged in water, displacing some of the water into a measuring cylinder as shown in Fig. 1.1.

Fig. 1.1 (not to scale)

The measured volume of displaced water is $(28.0 \pm 0.5) \mathrm{cm}^{3}$ .
Calculate:

[ 1 ]

(i)

the radius, in cm , of the sphere

radius =cm [1]

[ 1 ]

(a)

In the following list, underline all quantities that are SI base quantities.
charge
electric current
force
time

[ 1 ]

(a)

Table 1.1 lists some SI quantities. Complete the table by indicating with a tick ( $\checkmark$ ) which rows are SI base quantities.

Table 1.1

[ 1 ]

(b)

Use the definition of power to determine its SI base units.

[ 2 ]

[Maximum number: 6]

The drag force $F_{\mathrm{D}}$ acting on an object falling through air is given by

F_{\mathrm{D}}=\frac{1}{2} C \rho A v^{2}

where A is the cross-sectional area of the object,
v is the velocity of the object in the air,
$\rho$ is the density of the air and
C is a constant called the drag coefficient.

(a)

Use SI base units to show that the drag coefficient has no units.

[ 3 ]

(b)

The sphere is falling in air at a terminal velocity of 25 in SI base units. The density of the air is 1.2 in SI base units.
The diameter of the sphere is 0.060 in SI base units.
Use your answer in (c) to calculate the drag coefficient C for the sphere.

[ 3 ]

[Maximum number: 1]

The product of pressure and volume has the same SI base units as

A

energy.

B

force.

C

force.

D

$\frac{\text { force }}{\text { length }}$ .

(a)

The list below shows some SI quantities.
Underline the quantity that is not an SI base quantity.

[ 1 ]