Diese Aufgaben gibt es in ihrer Originalsprache.

1. Thema: Dimensions

   1. What are the dimensions of force?

   AMLT⁻²BMLT⁻¹CML²T⁻²DMT⁻²
   Lösung

   A. MLT⁻²

   • Force = mass × acceleration.
   • Acceleration has dimensions LT⁻², so force is MLT⁻².

2. Thema: Motion

   2. A car starts from rest and accelerates uniformly to 20 m/s in 5 s. How far does it travel?

   A100 mB4 mC25 mD50 m
   Lösung

   D. 50 m

   • Average velocity = (0 + 20) ÷ 2 = 10 m/s.
   • Distance = average velocity × time = 10 × 5 = 50 m.

3. Thema: Energy

   3. Find the kinetic energy of a 2 kg body moving at 3 m/s.

   A6 JB18 JC9 JD3 J
   Lösung

   C. 9 J

   • KE = ½mv².
   • = ½ × 2 × 3² = 9 J.

4. Thema: Free fall

   4. A stone is dropped from a height of 20 m. How long does it take to reach the ground? (g = 10 m/s²)

   A4 sB2 sC1 sD√2 s
   Lösung

   B. 2 s

   • h = ½gt², so t = √(2h/g).
   • t = √(2 × 20 ÷ 10) = √4 = 2 s.

5. Thema: Momentum

   5. Find the momentum of a 5 kg mass moving at 4 m/s.

   A20 kg m/sB1.25 kg m/sC40 kg m/sD9 kg m/s
   Lösung

   A. 20 kg m/s

   • Momentum = mass × velocity.
   • = 5 × 4 = 20 kg m/s.

6. Thema: Pressure

   6. Find the pressure due to water at a depth of 10 m. (Density of water = 1000 kg/m³, g = 10 m/s²)

   A1.0 × 10⁴ PaB1.0 × 10³ PaC1.0 × 10⁶ PaD1.0 × 10⁵ Pa
   Lösung

   D. 1.0 × 10⁵ Pa

   • P = hρg.
   • = 10 × 1000 × 10 = 100,000 Pa = 1.0 × 10⁵ Pa.

7. Thema: Heat

   7. How much heat is needed to raise the temperature of 2 kg of water by 10 °C? (Specific heat capacity of water = 4200 J/kg K)

   A42,000 JB8,400 JC84,000 JD840 J
   Lösung

   C. 84,000 J

   • Q = mcΔθ.
   • = 2 × 4200 × 10 = 84,000 J.

8. Thema: Gas laws

   8. A gas at 100 kPa occupies 6 L. It is compressed to 2 L at constant temperature. Find its new pressure.

   A33 kPaB300 kPaC200 kPaD600 kPa
   Lösung

   B. 300 kPa

   • Boyle's law: P₁V₁ = P₂V₂.
   • 100 × 6 = P₂ × 2, so P₂ = 300 kPa.

9. Thema: Waves

   9. A wave has a frequency of 50 Hz and a wavelength of 2 m. Find its speed.

   A100 m/sB25 m/sC52 m/sD0.04 m/s
   Lösung

   A. 100 m/s

   • v = fλ.
   • = 50 × 2 = 100 m/s.

10. Thema: Lenses

    10. An object is placed 15 cm from a converging lens of focal length 10 cm. Find the image distance.

    A6 cmB25 cmC5 cmD30 cm
    Lösung

    D. 30 cm

    • 1/f = 1/u + 1/v, so 1/v = 1/10 − 1/15.
    • 1/v = 3/30 − 2/30 = 1/30.
    • v = 30 cm (a real image on the other side of the lens).

11. Thema: Electricity

    11. Find the combined resistance of 6 Ω and 3 Ω connected in parallel.

    A9 ΩB4.5 ΩC2 ΩD18 Ω
    Lösung

    C. 2 Ω

    • 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6.
    • R = 6/3 = 2 Ω.

12. Thema: Electrical energy

    12. A 2 kW heater is used for 3 hours. How much energy does it use?

    A1.5 kWhB6 kWhC5 kWhD6000 kWh
    Lösung

    B. 6 kWh

    • Energy = power × time.
    • = 2 kW × 3 h = 6 kWh.

13. Thema: Radioactivity

    13. A radioactive sample of 64 g has a half-life of 4 days. How much remains after 12 days?

    A8 gB16 gC4 gD21.3 g
    Lösung

    A. 8 g

    • 12 days ÷ 4 days = 3 half-lives.
    • 64 → 32 → 16 → 8 g.

14. Thema: Photoelectric effect

    14. Photons of energy 5 eV fall on a metal with a work function of 2 eV. Find the maximum kinetic energy of the emitted electrons.

    A7 eVB2.5 eVC10 eVD3 eV
    Lösung

    D. 3 eV

    • Einstein's equation: KEmax = hf − W.
    • = 5 − 2 = 3 eV.

15. Thema: Transformers

    15. An ideal transformer has 100 turns on the primary and 500 turns on the secondary. The primary voltage is 240 V. Find the secondary voltage.

    A48 VB240 VC1200 VD600 V
    Lösung

    C. 1200 V

    • Vs/Vp = Ns/Np.
    • Vs = 240 × 500 ÷ 100 = 1200 V.