A) A car of mass 1000 kg travels round a circular track of radius 100 m at a speed of 10 m/s.

$$
a = \frac{(10 \, \text{m/s})^2}{100 \, \text{m}} = \frac{100 \, \text{m}^2/\text{s}^2}{100 \, \text{m}} = 1 \, \text{m/s}^2
$$
The acceleration of the car is $\boxed{\mathbf{1 \, \text{m/s}^2}}$.

• iii) The size of the force needed to cause the acceleration.

$$
F = (1000 \, \text{kg}) \times (1 \, \text{m/s}^2) = 1000 \, \text{N}
$$
The size of the force is $\boxed{\mathbf{1000 \, \text{N}}}$.

• iv) Give a reason why when roads are wet, cars sometimes slide out of the road when moving round a bend. When roads are wet, the coefficient of friction between the tires and the road decreases significantly. This reduces the maximum possible frictional force that can act as the centripetal force, making it insufficient to keep the car in its circular path, causing it to slide outwards.

• v) What modification could be made on the road to prevent the car from sliding out of the road. The road can be banked (tilted inwards) at the bend. This provides a component of the normal force that contributes to the centripetal force, reducing the reliance on friction.

1. b) i) Define Density?
Density is defined as the mass per unit volume of a substance. It is a measure of how much matter is packed into a given space.

1. b) ii) A measuring cylinder contains $60 \, \text{cm}^3$ of water. A metal block of mass $163.8 \, \text{g}$ is completely immersed in the water and the reading on the cylinder is found to increase to $81 \, \text{cm}^3$. Calculate the density of the block.

Volume of water $V_{\text{water}} = 60 \, \text{cm}^3$
Volume of water + block $V_{\text{total}} = 81 \, \text{cm}^3$
Volume of block $V_{\text{block}} = V_{\text{total}} - V_{\text{water}} = 81 \, \text{cm}^3 - 60 \, \text{cm}^3 = 21 \, \text{cm}^3$

Mass of block $m_{\text{block}} = 163.8 \, \text{g}$

The density of the block is $\boxed{\mathbf{7.8 \, \text{g/cm}^3}}$.

1. c) Keldy and Meldy sit on opposite sides of a see saw of negligible weight and it balances horizontally. If Meldy weighs $400 \, \text{N}$ and sits $2.7 \, \text{m}$ away from the pivot as shown in Figure 1 below. Keldy weighs $300 \, \text{N}$.

• i) State the principle of moments. The principle of moments states that for an object to be in rotational equilibrium (balanced), the sum of the clockwise moments about any pivot point must be equal to the sum of the anticlockwise moments about the same pivot point.

• ii) Calculate distance X.

$$
300X = 1080
$$
$$
X = \frac{1080}{300} = 3.6 \, \text{m}
$$
Distance X is $\boxed{\mathbf{3.6 \, \text{m}}}$.

2. a) State Ohm's law.
Ohm's law states that the current flowing through a metallic conductor is directly proportional to the potential difference (voltage) across its ends, provided that its temperature and other physical conditions remain constant. Mathematically, this is expressed as $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance.

2. b) Figure 2 shows a network of 3 resistors connected to a battery of E. m. f. $28 \, \text{V}$.

• i) Name the meters labeled Y and Z. Meter Y is connected in parallel across the battery, so it is a voltmeter. Meter Z is connected in series with the $5 \, \Omega$ resistor, so it is an ammeter. Y: $\boxed{\text{Voltmeter}}$ Z: $\boxed{\text{Ammeter}}$

• ii) What property of Meter Y enables it to be connected as shown? A voltmeter (Meter Y) has a very high internal resistance. This property ensures that when connected in parallel across a component, it draws a negligible amount of current from the circuit, thus not significantly altering the potential difference it is measuring.

• iii) The total resistance in the circuit.

$$
R_{\text{total}} = 5 \, \Omega + R_p = 5 \, \Omega + 2 \, \Omega = 7 \, \Omega
$$
The total resistance in the circuit is $\boxed{\mathbf{7 \, \Omega}}$.

• iv) The reading of meter Y. Meter Y is a voltmeter connected across the battery. Assuming the battery is ideal (no internal resistance), the voltmeter will read the electromotive force (E.m.f.) of the battery. The reading of meter Y is $\boxed{\mathbf{28 \, \text{V}}}$.

• v) The reading of meter Z. Meter Z is an ammeter measuring the total current flowing through the main circuit (which passes through the $5 \, \Omega$ resistor).

$$
I = \frac{28 \, \text{V}}{7 \, \Omega} = 4 \, \text{A}
$$
The reading of meter Z is $\boxed{\mathbf{4 \, \text{A}}}$.

2. c) Figure 3 is an example of a logic gate.
The image for Figure 3 is not provided, so this question cannot be answered.