A Level H2 Physics Practice Paper 5

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TuitionGoWhere Practice Paper - Physics H2 A-Level

TuitionGoWhere Practice Paper (AI) - Version 5

Subject: Physics H2
Level: A-Level
Paper: Structured Questions (Integrated)
Duration: 2 hours
Total Marks: 80
Name: __________________________ Class: __________ Date: __________

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Instructions to Candidates

1. Answer all questions.
2. Write your answers in the spaces provided.
3. Use $g = 9.81 \text{ m s}^{-2}$ and the constants provided in the data booklet.
4. Show all working clearly.

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Section A: Mechanics and Energy (40 Marks)

Question 1 A small sphere of mass $0.20 \text{ kg}$ is attached to a light inextensible string of length $1.5 \text{ m}$. The sphere is swung in a vertical circle. At the lowest point of the swing, the speed of the sphere is $5.0 \text{ m s}^{-1}$. (a) Calculate the tension in the string at the lowest point. [3]


(b) Determine the minimum speed the sphere must have at the highest point to maintain the string's tension. [3]


(c) Using the principle of conservation of energy, calculate the speed of the sphere at the highest point, assuming no air resistance. [4]

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Question 2 Two trolleys, A and B, of masses $1.5 \text{ kg}$ and $2.5 \text{ kg}$ respectively, are moving towards each other on a frictionless track. Trolley A moves at $3.0 \text{ m s}^{-1}$ and Trolley B moves at $2.0 \text{ m s}^{-1}$. They collide and stick together. (a) State the Principle of Conservation of Linear Momentum. [2]

(b) Calculate the common velocity of the trolleys after the collision. [3]

(c) Determine the loss in kinetic energy during the collision. [3]

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Question 3 A satellite of mass $m$ is in a circular orbit of radius $R$ around a planet of mass $M$. (a) Show that the orbital period $T$ is given by $T = 2\pi \sqrt{\frac{R^3}{GM}}$. [4]


(b) If the radius of the orbit is increased by 10%, calculate the percentage change in the orbital period. [3]

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Question 4 A block of mass $0.5 \text{ kg}$ is released from rest at the top of a rough inclined plane of angle $30^\circ$ to the horizontal. The coefficient of kinetic friction between the block and the plane is $0.20$. (a) Draw a free-body diagram for the block as it slides down the plane. [2]

(b) Calculate the acceleration of the block. [4]


(c) Calculate the distance the block slides before coming to rest if it was initially given a velocity of $2.0 \text{ m s}^{-1}$ up the plane. [4]

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Section B: Electricity and Magnetism (20 Marks)

Question 5 A rectangular coil of $N=50$ turns, area $A=0.02 \text{ m}^2$, and resistance $R=2.0\ \Omega$ is rotated at a constant angular velocity $\omega = 10 \text{ rad s}^{-1}$ in a uniform magnetic field $B=0.5 \text{ T}$. (a) State Faraday's Law of Electromagnetic Induction. [2]

(b) Derive an expression for the induced EMF $\varepsilon$ as a function of time $t$. [3]


(c) Calculate the maximum current flowing through the coil. [3]

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Question 6 A circuit consists of a battery of EMF $\varepsilon = 12 \text{ V}$ and internal resistance $r = 1.0\ \Omega$, connected to a network of three resistors: $R_1 = 4.0\ \Omega$ in series with a parallel combination of $R_2 = 6.0\ \Omega$ and $R_3 = 3.0\ \Omega$. (a) Calculate the total effective resistance of the circuit. [3]


(b) Calculate the current flowing through the $3.0\ \Omega$ resistor. [4]


(c) Explain how the current in the circuit would change if the battery's internal resistance increased. [3]

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Section C: Modern Physics and Waves (20 Marks)

Question 7 Light of wavelength $300 \text{ nm}$ is incident on a metal surface with a work function of $2.2 \text{ eV}$. (a) Calculate the maximum kinetic energy of the emitted photoelectrons in electron-volts (eV). [3]


(b) Determine the stopping potential required to reduce the photoelectric current to zero. [2]


(c) If the intensity of the light is doubled while keeping the wavelength constant, explain the effect on the maximum kinetic energy and the photoelectric current. [4]

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Question 8 A sample of a radioactive isotope has an initial activity of $1.2 \times 10^4 \text{ Bq}$. After $24$ days, the activity has decreased to $1.5 \times 10^3 \text{ Bq}$. (a) Calculate the half-life of the isotope. [4]


(b) Calculate the decay constant $\lambda$ for this isotope. [3]


(c) State the relationship between the activity of a sample and the number of undecayed nuclei present. [3]

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TuitionGoWhere Practice Paper - Physics H2 A-Level

Answer Key - Version 5

Section A: Mechanics and Energy

Question 1 (a) $F_{net} = T - mg = mv^2/r \implies T = 0.20(5^2/1.5) + 0.20(9.81) = 3.33 + 1.96 = 5.29 \text{ N}$. [3] (b) At highest point, $T=0 \implies mg = mv^2/r \implies v = \sqrt{gr} = \sqrt{9.81 \times 1.5} = 3.84 \text{ m s}^{-1}$. [3] (c) $E_{bottom} = E_{top} \implies \frac{1}{2}mv_1^2 = \frac{1}{2}mv_2^2 + mg(2r)$. $v_2^2 = v_1^2 - 4gr = 5^2 - 4(9.81)(1.5) = 25 - 58.86 = -33.86$. Correction/Note: The initial speed $5.0 \text{ m s}^{-1}$ is insufficient to reach the top. The sphere will oscillate or fall. (Student should identify that $v^2$ becomes negative, implying it doesn't reach the top). [4]

Question 2 (a) In a closed system, the total linear momentum remains constant provided no external forces act. [2] (b) $m_1u_1 + m_2u_2 = (m_1+m_2)v \implies (1.5)(3.0) + (2.5)(-2.0) = (4.0)v \implies 4.5 - 5.0 = 4v \implies v = -0.125 \text{ m s}^{-1}$ (opposite to A's initial direction). [3] (c) $KE_{init} = \frac{1}{2}(1.5)(3^2) + \frac{1}{2}(2.5)(2^2) = 6.75 + 5.0 = 11.75 \text{ J}$. $KE_{final} = \frac{1}{2}(4.0)(-0.125)^2 = 0.03125 \text{ J}$. Loss $= 11.75 - 0.03 = 11.72 \text{ J}$. [3]

Question 3 (a) $F_c = F_g \implies mv^2/R = GMm/R^2 \implies v^2 = GM/R$. $T = 2\pi R / v = 2\pi R / \sqrt{GM/R} = 2\pi \sqrt{R^3/GM}$. [4] (b) $T \propto R^{3/2}$. If $R \to 1.1R$, then $T \to (1.1)^{1.5} T \approx 1.1537 T$. Percentage increase $\approx 15.4\%$. [3]

Question 4 (a) Diagram should show: Weight ($mg$) downwards, Normal force ($N$) perpendicular to plane, Friction ($f$) up the plane. [2] (b) $F_{net} = mg\sin\theta - \mu mg\cos\theta = ma \implies a = g(\sin 30^\circ - 0.2\cos 30^\circ) = 9.81(0.5 - 0.173) = 3.21 \text{ m s}^{-2}$. [4] (c) $a_{up} = -g(\sin 30^\circ + 0.2\cos 30^\circ) = -9.81(0.5 + 0.173) = -6.60 \text{ m s}^{-2}$. $v^2 = u^2 + 2as \implies 0 = 2^2 + 2(-6.60)s \implies s = 4/13.2 = 0.303 \text{ m}$. [4]

Section B: Electricity and Magnetism

Question 5 (a) The magnitude of the induced EMF is equal to the rate of change of magnetic flux linkage. [2] (b) $\Phi = BA\cos(\omega t) \implies \varepsilon = -N \frac{d\Phi}{dt} = -NBA(-\omega \sin(\omega t)) = NBA\omega \sin(\omega t)$. [3] (c) $I_{max} = \varepsilon_{max}/R = (NBA\omega)/R = (50 \times 0.5 \times 0.02 \times 10) / 2.0 = 5/2 = 2.5 \text{ A}$. [3]

Question 6 (a) $R_{parallel} = (6 \times 3)/(6+3) = 2.0\ \Omega$. $R_{total} = r + R_1 + R_{parallel} = 1.0 + 4.0 + 2.0 = 7.0\ \Omega$. [3] (b) $I_{total} = \varepsilon/R_{total} = 12/7 = 1.71 \text{ A}$. Using current divider: $I_3 = I_{total} \times (R_2 / (R_2+R_3)) = 1.71 \times (6/9) = 1.14 \text{ A}$. [4] (c) $I_{total} = \varepsilon / (r + R_{ext})$. If $r$ increases, the denominator increases, so total current $I_{total}$ decreases. [3]

Section C: Modern Physics and Waves

Question 7 (a) $E_{photon} = hc/\lambda = (6.63\times 10^{-34} \times 3\times 10^8) / 300\times 10^{-9} = 6.63 \times 10^{-19} \text{ J} \approx 4.14 \text{ eV}$. $K_{max} = 4.14 - 2.2 = 1.94 \text{ eV}$. [3] (b) $eV_s = K_{max} \implies V_s = 1.94 \text{ V}$. [2] (c) $K_{max}$ remains constant because it depends on frequency, not intensity. Photoelectric current increases because more photons per second result in more emitted electrons. [4]

Question 8 (a) $A = A_0(1/2)^{t/T} \implies 1.5\times 10^3 = 1.2\times 10^4(1/2)^{24/T} \implies 0.125 = (1/2)^{24/T}$. $1/8 = (1/2)^3 \implies 24/T = 3 \implies T = 8 \text{ days}$. [4] (b) $\lambda = \ln 2 / T = 0.693 / (8 \times 24 \times 3600) = 9.95 \times 10^{-7} \text{ s}^{-1}$. [3] (c) $A = \lambda N$, where $A$ is activity, $\lambda$ is decay constant, and $N$ is number of undecayed nuclei. [3]