(a)

A square solar panel with sides of length 1300 mm is shown in Fig. 1.1.

Fig. 1.1 (not to scale)

Light is incident normally on the solar panel.

[ 2 ]

(i)

The power of the light incident on the solar panel is 750 W .

Calculate the intensity of the light.

\text { intensity = \mathrm{Wm}^{-2}

[ 2 ]

[Maximum number: 4]

The drag force $F_{\mathrm{D}}$ acting on a sphere falling through a liquid is given by

F_{\mathrm{D}}=6 \pi \eta r v

where r is the radius of the sphere,
v is the speed of the sphere in the liquid and
$\eta$ is a property of the liquid called the viscosity.

(a)

(i)

The density of the liquid is $920 \mathrm{~kg} \mathrm{~m}^{-3}$ .

Show that the upthrust acting on the sphere is 1.0 N .

[ 2 ]

(ii)

Calculate the mass of the sphere.
mass = kg

[ 2 ]

(a)

(i)

Define pressure.

[ 1 ]

(ii)

Use the answer to (a)(i) to show that the SI base units of pressure are $\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2}$ .

[ 1 ]

[Maximum number: 1]

A0.10 kg mass is taken to Mars and then weighed on a spring balance and on a lever balance. The acceleration due to gravity on Mars is 38\% of its value on Earth.

What are the readings on the two balances on Mars? (Assume that on Earth $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ .)

spring

balance/N

lever

balance/kg

0.38

0.038

0.38

0.10

1.0

0.038

1.0

0.10

[Maximum number: 2]

Calculate, using Newton's law of gravitation, the gravitational force on the stone.
gravitational force = N [2]
2. Determine the force required to maintain the stone in its circular path.
force = N

(a)

The Earth may be considered to be a uniform sphere of radius $6.37 \times 10^{3} \mathrm{~km}$ with its mass of $5.98 \times 10^{24} \mathrm{~kg}$ concentrated at its centre. The Earth spins on its axis with a period of 24.0 hours.

(i)

The stone is now hung from a newton-meter.

Use your answers in (i) to determine the reading on the meter. Give your answer to three significant figures.

[Maximum number: 3]

A sphere of radius 2.1 mm falls with terminal (constant) velocity through a liquid, as shown in Fig. 1.1.

Fig. 1.1

Three forces act on the moving sphere. The weight of the sphere is $7.2 \times 10^{-4} \mathrm{~N}$ and the upthrust acting on it is $4.8 \times 10^{-4} \mathrm{~N}$ . The viscous force $F_{\mathrm{V}}$ acting on the sphere is given by

F_{\mathrm{V}}=k r v

where r is the radius of the sphere, v is its velocity and k is a constant. The value of k in SI units is 17 .

(a)

Use the value of the upthrust acting on the sphere to calculate the density $\rho$ of the liquid.
$\rho=$ $\mathrm{kg} \mathrm{m}^{-3}$

[ 3 ]

[Maximum number: 1]

A stone sinks in water.
What is a possible value for the density of the stone?

A

$8 \times 10^{2} \mathrm{~kg} \mathrm{~m}^{-3}$

B

$2 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$

C

$8 \times 10^{3} \mathrm{Nm}^{-3}$

D

$2 \times 10^{4} \mathrm{Nm}^{-3}$

(a)

Define density.

[ 1 ]

(b)

Explain how the difference in the densities of solids, liquids and gases may be related to the spacing of their molecules.

[ 2 ]

(c)

A paving slab has a mass of 68 kg and dimensions $50 \mathrm{~mm} \times 600 \mathrm{~mm} \times 900 \mathrm{~mm}$ .

[ 5 ]

(i)

Calculate the density, in $\mathrm{kg} \mathrm{m}^{-3}$ , of the material from which the paving slab is made.
density = $\mathrm{kg} \mathrm{m}^{-3}$

[ 2 ]

(ii)

Calculate the maximum pressure a slab could exert on the ground when resting on one of its surfaces.
pressure = Pa

[ 3 ]

(a)

A uniform cylinder has diameter D, length L and mass M.

The density $\rho$ of the cylinder is given by

\rho=\frac{4 M}{\pi D^{2} L} .

Table 1.2 shows the data obtained from an experiment to determine the density of the cylinder.

Table 1.2

[ 2 ]

(i)

Calculate the density of the cylinder. Give your answer to three significant figures.
density = $\mathrm{kg} \mathrm{m}^{-3}$

[ 2 ]

[Maximum number: 3]

A solid metal sphere has a diameter of $(3.42 \pm 0.02) \mathrm{cm}$ and a mass of $(67 \pm 2) \mathrm{g}$ .

(a)

Calculate the density, in $\mathrm{g} \mathrm{cm}^{-3}$ , of the metal.

\text { density =g cm }{ }^{-3} \text { [3] }

[ 3 ]

Question 1

Question 1(b)

Question 1(b)(i)

Question 1

Question 1(d)

Question 1(d)(i)

Question 1(d)(ii)

Question 1

Question 1(a)

Question 1(a)(i)

Question 1(a)(ii)

Question 1

Question 1

Question 1(a)

Question 1(a)(ii)

Question 1

Question 1(b)

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(c)(i)

Question 1(c)(ii)

Question 1

Question 1(b)

Question 1(b)(ii)

Question 1

Question 1(a)