A Level Physics: Constants and Formulae

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Questions and Answers

Which of the following is the correct equation for gravitational force (F) between two point masses $m_1$ and $m_2$ separated by a distance r?

  • $F = G \frac{m_1 m_2}{r^2}$ (correct)
  • $F = G \frac{m_1^2 m_2^2}{r^2}$
  • $F = G \frac{m_1 + m_2}{r^2}$
  • $F = G \frac{m_1 m_2}{r}$

A geostationary orbit requires a satellite to orbit in any plane as long as its period is 24 hours and it maintains a fixed position relative to Earth.

False (B)

Besides the density of a liquid, list two other physical properties of materials that can be used for measuring temperature.

Any two of: Thermoelectric properties, resistance, volume

In a mercury thermometer, temperature measurement relies on the principle that the _______ of mercury varies with temperature.

<p>density</p>
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Match the properties mentioned with their applications in temperature measurement:

<p>Thermoelectric properties = Thermocouples Resistance = Resistance thermometers Volume change of a liquid = Liquid-in-glass thermometer Infrared Radiation = Infrared Thermometers</p>
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What is the defining equation for simple harmonic motion (SHM)?

<p>$a = -ω^2x$ (C)</p>
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In simple harmonic motion, damping always increases the angular frequency of the oscillations.

<p>False (B)</p>
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In the context of oscillations, what is meant by 'damping'?

<p>The loss of energy from an oscillating system, causing the amplitude to decrease over time.</p>
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In a system undergoing oscillations, if the oscillations are lightly damped, it means that the damping force is _______, leading to a gradual decrease in amplitude.

<p>small</p>
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Match the following terms with their definitions relating to electric fields:

<p>Electric Field Line = Represents the direction of the force on a positive test charge at that point Electric Field Strength = Force per unit positive charge Potential Difference = Work done in moving a unit positive charge between two points</p>
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What does the direction of an electric field line indicate?

<p>The direction of the force on a positive test charge (C)</p>
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The electric field is always the same regardless of the charge or mass of the particle entering the region between the plates.

<p>False (B)</p>
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If a proton and a helium nucleus enter an electric field with the same initial velocity, explain how their final speeds compare after leaving the region of the electric field.

<p>Because the helium nucleus has a greater mass (and the same charge), its acceleration will be smaller. Therefore, its final speed will be smaller than the proton's final speed</p>
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The two-way switch S is initially at position X. Once moved to position Y, the capacitor _______ through wire P.

<p>discharges</p>
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Match the following circuit components with their effects on the time constant (\tau) of a discharging RC circuit:

<p>Increase in resistance = Increases (\tau) Increase in capacitance = Increases (\tau) Decrease in resistance = Decreases (\tau) Decrease in capacitance = Decreases (\tau)</p>
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In the equation $V_H = \frac{BI}{ntq}$ for Hall voltage, what does 'n' represent?

<p>Number density of charge carriers (C)</p>
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A thicker slice of material in a Hall probe increases the Hall voltage.

<p>False (B)</p>
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In the context of the Hall effect, explain why a thin slice of material is used in a Hall probe.

<p>A thin slice increases the Hall voltage because the Hall voltage is inversely proportional to the thickness of the slice</p>
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In a sinusoidal alternating voltage, the ____________ voltage is the root-mean-square voltage multiplied by √2.

<p>peak</p>
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Match the terms with the types of energy associated with them:

<p>Piezoelectric Crystal = Mechanical and electrical Radiation = Electromagnetic Electron = Kinetic Metal = Work function energy</p>
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What happens to the air surrounding a piezoelectric crystal when an alternating voltage is applied to it?

<p>The air vibrates due to the crystal's oscillations (B)</p>
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Increasing the frequency of incident radiation while keeping the power constant increases the rate of emission of photoelectrons.

<p>False (B)</p>
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What is meant by the 'work function energy' of a metal?

<p>The minimum energy required to remove an electron from the surface of the metal.</p>
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The radiant flux intensity of a star observed from Earth _______ as the distance from Earth increases.

<p>decreases</p>
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Which process is characterized as both random and spontaneous?

<p>Radioactive Decay (B)</p>
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Flashcards

Gravitational Force

The force between two point masses, proportional to the product of their masses and inversely proportional to the square of the distance between them.

Orbital Period

The time taken for a satellite to complete one orbit around a celestial body.

Geostationary Orbit

An orbit where a satellite remains in the same position relative to a rotating planet.

Temperature

Property related to the average kinetic energy of the particles in a system.

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Thermodynamic Temperature Scale

The temperature scale where zero is absolute zero, and units are the same size as Celsius.

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Defining equation for SHM

Equation that relates acceleration to displacement in SHM.

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Amplitude (oscillations)

The maximum displacement from the equilibrium position in oscillatory motion.

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Damping

Loss of energy from an oscillating system, usually due to friction.

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Electric Field

A field that exerts a force on charged particles.

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Capacitance

The amount of charge stored per unit potential difference across it.

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Time Constant (Capacitor)

The time taken for the current or voltage in a discharging capacitor to fall to approximately 37% of its initial value.

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Hall Voltage

A voltage produced across a conductor when a magnetic field is applied perpendicular to the current flow.

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Work Function

Minimum energy needed to remove an electron from a metal surface.

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Luminosity

Total power radiated by a star.

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Random Decay

Decay where the time of decay of individual nuclei cannot be predicted.

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Spontaneous Decay

Decay unaffected by external conditions.

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Study Notes

  • This is the Cambridge Assessment International Education, Cambridge International AS & A Level PHYSICS paper 9702/41 for October/November 2022.
  • The exam duration is 2 hours.
  • The total mark for this paper is 100.

Data

  • Acceleration of free fall (g) is 9.81 m s⁻².
  • Speed of light in free space (c) is 3.00 x 10⁸ m s⁻¹.
  • Elementary charge (e) is 1.60 x 10⁻¹⁹ C.
  • Unified atomic mass unit (1 u) is 1.66 × 10⁻²⁷ kg.
  • Rest mass of proton (mp) is 1.67 x 10⁻²⁷ kg.
  • Rest mass of electron (me) is 9.11 x 10⁻³¹ kg.
  • Avogadro constant (Nₐ) is 6.02 × 10²³ mol⁻¹.
  • Molar gas constant (R) is 8.31 J K⁻¹ mol⁻¹.
  • Boltzmann constant (k) is 1.38 x 10⁻²³ J K⁻¹.
  • Gravitational constant (G) is 6.67 × 10⁻¹¹ N m² kg⁻².
  • Permittivity of free space (ε₀) is 8.85 x 10⁻¹² F m⁻¹ and (1/(4πε₀)) is 8.99 × 10⁹ m F⁻¹.
  • Planck constant (h) is 6.63 x 10⁻³⁴ Js.
  • Stefan-Boltzmann constant (σ) is 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

Formulae

  • Uniformly accelerated motion equations: s = ut + (1/2)at², v² = u² + 2as.
  • Hydrostatic pressure: Δp = ρgh.
  • Upthrust: F = ρgV.
  • Doppler effect for sound waves: f₀ = fₛ(v/(v ± vₛ)).
  • Electric current: I = Anvq.
  • Resistors in series: R = R₁ + R₂ + ...
  • Resistors in parallel: 1/R = 1/R₁ + 1/R₂ + ...
  • Gravitational potential (Φ) is GM/r.
  • Gravitational potential energy (Eₚ) is -GMm/r.
  • Pressure of an ideal gas: p = (1/3)(N/V)⟨c²⟩.
  • Simple harmonic motion: a = -ω²x.
  • Velocity of particle in s.h.m.: v = v₀cosωt and v = ±ω√(x₀² - x²).
  • Electric potential (V) is Q/(4πε₀r).
  • Electrical potential energy (Eₚ) is Qq/(4πε₀r).
  • Capacitors in series: 1/C = 1/C₁ + 1/C₂ + ...
  • Capacitors in parallel: C = C₁ + C₂ + ...
  • Discharge of a capacitor: x = x₀e^(-t/RC).
  • Hall voltage: Vᴴ = BI/(ntq).
  • Alternating current/voltage: x = x₀sinωt.
  • Radioactive decay: x = x₀e^(-λt).
  • Decay constant: λ = 0.693/t₁/₂.
  • Intensity reflection coefficient: Iᵣ/I₀ = (Z₁ - Z₂)² / (Z₁ + Z₂)²
  • Stefan-Boltzmann law: L = 4πσr²T⁴.
  • Doppler redshift: Δλ/λ ≈ Δf/f ≈ v/c.

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