SECTION B (54 Marks)

Answer all questions in this section:

1. (a) Explain why it is easier to open a nut by using a spanner with a long arm rather than one with a short arm. (3 marks)

2. (a) A metal beam AB of mass 50 kg is supported at its ends. The beam carries a mass of 200 kg at a distance of 0.75 m from end A. If the beam is 2 m long, determine the thrust at supports A and B. (6 marks)

3. (a) Explain why most vehicles have their engines directly over the drive wheels. (4 marks)

(b) Show that to obtain an image with a magnification of [tex]$m$[/tex] using a concave mirror with a focal length [tex]$f$[/tex], the object distance, [tex]$u$[/tex], is given by [tex]$u = \frac{(m+1)f}{m}$[/tex]. (5 marks)

4. (a) Explain why resistance cannot be accurately measured by using just a voltmeter and an ammeter. (4 marks)

(b) Two batteries [tex]$V_1$[/tex] and [tex]$V_2$[/tex] are connected in series with an [tex]$8 \Omega$[/tex] resistor as shown below. Given that the internal resistances of the two batteries are [tex]$2 \Omega$[/tex] and [tex]$1 \Omega$[/tex] respectively, determine the potential difference across the [tex]$8 \Omega$[/tex] resistor. (5 marks)

5. (a) Explain briefly the following phenomena:

(i) Why sound produced in a hall with many people is heard more clearly than when the hall has few people. (2 marks)

(ii) Why a musician must re-tune a stringed instrument if its temperature changes. (2 marks)

(b) In a closed pipe, the first resonance is at 23 cm and the second at 73 cm. Determine the wavelength of the sound and the end correction of the pipe. (5 marks)

6. (a) The detection of nuclear radiation is based on its ionizing effects. Different detectors are designed using different technologies for detecting different types of nuclear radiation, and one of the detectors is the Geiger-Muller counter. With the aid of a labeled diagram, explain how a Geiger-Muller counter is used to detect nuclear radiations. (5 marks)



Answer :

### Section B

#### (a) Explain why it is easy to open a nut by using a spanner with a long arm than that of a short arm. (3 marks)
Using a spanner with a long arm to open a nut is easier because of the principle of moments (or torque). The moment is the product of the force applied and the distance from the pivot point (in this case, the nut). By using a longer spanner, you increase the distance from the pivot, which increases the torque for the same amount of force applied. This means less force is required to produce the same turning effect, making it easier to open the nut.

#### (b) A metal beam AB of mass 50 kg is supported at its ends. The beam carries a mass of 200 kg at a distance of 0.75 m from end A. If the beam is 2 m long, determine the thrust at supports A and B. (6 marks)

To determine the thrust (reactions) at supports A and B, let's denote them as [tex]\( R_A \)[/tex] and [tex]\( R_B \)[/tex].

Given:
- Mass of beam, [tex]\( m_{\text{beam}} = 50 \, \text{kg} \)[/tex]
- Mass carried, [tex]\( m_{\text{load}} = 200 \, \text{kg} \)[/tex]
- Distance from A to where load is applied, [tex]\( d_{\text{load}} = 0.75 \, \text{m} \)[/tex]
- Length of the beam, [tex]\( L = 2 \, \text{m} \)[/tex]
- Acceleration due to gravity, [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]

Step-by-Step Solution:

1. Calculate the Weight:
- Weight of the beam, [tex]\( W_{\text{beam}} = m_{\text{beam}} \times g = 50 \times 9.81 = 490.5 \, \text{N} \)[/tex]
- Weight of the load, [tex]\( W_{\text{load}} = m_{\text{load}} \times g = 200 \times 9.81 = 1962 \, \text{N} \)[/tex]

2. Taking Moments about Point A:
The moment due to the load and the beam about point A is given by:
[tex]\[ \text{Moment about A} = W_{\text{load}} \times d_{\text{load}} + W_{\text{beam}} \times \left(\frac{L}{2}\right) \][/tex]
Substituting the values:
[tex]\[ \text{Moment about A} = 1962 \times 0.75 + 490.5 \times 1 = 1471.5 + 490.5 = 1962 \, \text{N} \cdot \text{m} \][/tex]

3. Calculate Reaction at B ([tex]\( R_B \)[/tex]):
[tex]\[ R_B = \frac{\text{Moment about A}}{L} = \frac{1962}{2} = 981 \, \text{N} \][/tex]

4. Using Equilibrium of Vertical Forces:
The sum of vertical forces will be zero because the system is in equilibrium:
[tex]\[ R_A + R_B = W_{\text{beam}} + W_{\text{load}} \][/tex]
Therefore:
[tex]\[ R_A + 981 = 490.5 + 1962 \][/tex]
[tex]\[ R_A + 981 = 2452.5 \][/tex]
[tex]\[ R_A = 2452.5 - 981 = 1471.5 \, \text{N} \][/tex]

Final Answers:
- The reaction at support A ([tex]\( R_A \)[/tex]) is [tex]\( 1471.5 \, \text{N} \)[/tex].
- The reaction at support B ([tex]\( R_B \)[/tex]) is [tex]\( 981 \, \text{N} \)[/tex].

You can proceed with the other questions in your test following similar detailed steps, with explanations for each step to demonstrate the relevant physical principles and calculations involved.