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

1. a) A car of mass 1000 \, kg travels round a circular track of radius 100 \, m at a speed of 10 \, m/s. i) State the name of the force that keeps the car in circular track. The force that keeps the car in a circular track is the centripetal force. This force is provided by the friction between the tires and the road. The name of the force is Centripetal force. ii) The acceleration of the car. Step 1: Identify the given values. Mass m = 1000 \, kg Radius r = 100 \, m Speed v = 10 \, m/s Step 2: Use the formula for centripetal acceleration. a = (v^2)/(r) Step 3: Substitute the values and calculate. a = (10 \, m/s)^2100 \, m = 100 \, m^2/s^2100 \, m = 1 \, m/s^2 The acceleration of the car is 1 \, m/s^2. iii) The size of the force needed to cause the acceleration. Step 1: Use Newton's second law for centripetal force. F = ma Step 2: Substitute the mass and the acceleration calculated in part (ii). F = (1000 \, kg) × (1 \, m/s^2) = 1000 \, N The size of the force is 1000 \, 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 \, cm^3 of water. A metal block of mass 163.8 \, g is completely immersed in the water and the reading on the cylinder is found to increase to 81 \, cm^3. Calculate the density of the block. Step 1: Calculate the volume of the metal block. Volume of water V_water = 60 \, cm^3 Volume of water + block V_total = 81 \, cm^3 Volume of block V_block = V_total - V_water = 81 \, cm^3 - 60 \, cm^3 = 21 \, cm^3 Step 2: Identify the mass of the block. Mass of block m_block = 163.8 \, g Step 3: Calculate the density of the block using the formula Density = MassVolume. Density = 163.8 \, g21 \, cm^3 = 7.8 \, g/cm^3 The density of the block is 7.8 \, 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 \, N and sits 2.7 \, m away from the pivot as shown in Figure 1 below. Keldy weighs 300 \, 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. Step 1: Identify the forces and distances from the pivot. Keldy's weight (anticlockwise force) F_Keldy = 300 \, N Keldy's distance from pivot X Meldy's weight (clockwise force) F_Meldy = 400 \, N Meldy's distance from pivot d_Meldy = 2.7 \, m Step 2: Apply the principle of moments (Anticlockwise moment = Clockwise moment). F_Keldy × X = F_Meldy × d_Meldy 300 \, N × X = 400 \, N × 2.7 \, m Step 3: Solve for X. 300X = 1080 X = (1080)/(300) = 3.6 \, m Distance X is 3.6 \, 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 \, 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 \, resistor, so it is an ammeter. Y: Voltmeter Z: 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. Step 1: Calculate the equivalent resistance of the parallel combination (6 \, and 3 \, ). (1)/(R_p) = (1)/(6 \, ) + (1)/(3 \, ) (1)/(R_p) = (1)/(6 \, ) + (2)/(6 \, ) = (3)/(6 \, ) = (1)/(2 \, ) R_p = 2 \, Step 2: Calculate the total resistance by adding the series resistor (5 \, ) to the parallel equivalent resistance. R_total = 5 \, + R_p = 5 \, + 2 \, = 7 \, The total resistance in the circuit is 7 \, . 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 28 \, 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 \, resistor). Step 1: Use Ohm's law I = (V)/(R_total). Voltage V = 28 \, V (E.m.f. of the battery) Total resistance R_total = 7 \, (calculated in part iii) Step 2: Substitute the values. I = 28 \, V7 \, = 4 \, A The reading of meter Z is 4 \, 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. What's next?