Practice waec model questions vol1 physics 2021 Past Questions

Question 1 View Details

Two point charges are placed on the x‑axis. Charge Q₁=+6 µC is at the origin and charge Q₂=‑3 µC is at x=0.40 m. (a) Find the position on the x‑axis where the net electric field is zero. (b) Calculate the electric potential at that point due to both charges. Give the potential in volts (use k=9.0×10⁹ N·m²·C⁻²).

Correct A. 1.16×10⁴ V

B. 9.5×10³ V

C. 1.05×10⁴ V

D. 1.30×10⁴ V

Correct Answer: A

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Question 2 View Details

A rectangular coil of 20 turns has dimensions 0.10 m (width) × 0.20 m (length). It moves with constant speed v into a uniform magnetic field of magnitude 0.50 T that is directed into the page. The plane of the coil remains perpendicular to the field. When the coil is half inside the field region the measured induced emf is 0.80 V. The total resistance of the coil is 2.0 Ω. (a) Determine the speed v of the coil. (b) Find the magnitude of the magnetic force acting on the coil at that instant (assume the induced current opposes the motion).

A. v = 0.25 m\/s; F = 0.50 N

B. v = 0.40 m\/s; F = 0.60 N

C. v = 0.55 m\/s; F = 0.90 N

Correct D. v = 0.40 m/s; F = 0.80 N

Correct Answer: D

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Question 3 View Details

A hydrogen atom initially at rest in vacuum emits a photon when an electron drops from the n=3 to the n=2 level. (a) Calculate the wavelength of the emitted photon. (b) Using conservation of momentum, determine the recoil speed of the hydrogen atom after the emission. (Use R=1.097×10⁷ m⁻¹, h=6.626×10⁻³⁴ J·s, c=3.00×10⁸ m s⁻¹, and the mass of a hydrogen atom 1.67×10⁻²⁷ kg.)

A. λ = 6.30×10⁻⁷ m; recoil speed = 0.68 m\/s

B. λ = 5.87×10⁻⁷ m; recoil speed = 0.72 m\/s

Correct C. λ = 6.56×10⁻⁷ m; recoil speed = 0.60 m/s

D. λ = 7.12×10⁻⁷ m; recoil speed = 0.55 m\/s

Correct Answer: C

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Question 4 View Details

A 5.0 kg block rests on a horizontal rough surface (μ_s=0.40, μ_k=0.30). It is attached to a 3.0 kg hanging mass by a light inextensible string over a smooth pulley. Determine (a) the acceleration of the system and (b) the tension in the string. (Take g=9.8 m s⁻².)

A. a = 2.30 m\/s²; T = 20.0 N

Correct B. a = 1.84 m/s²; T = 23.9 N

C. a = 2.10 m\/s²; T = 21.5 N

D. a = 1.55 m\/s²; T = 26.3 N

Correct Answer: B

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Question 5 View Details

A motion diagram shows a car moving in a straight line with its positions recorded at equal 1 s intervals: at t=0 s the car is at 0 m, at t=1 s at 2 m, at t=2 s at 6 m, at t=3 s at 12 m and at t=4 s at 20 m. Assuming the car moves with constant acceleration, determine the magnitude of that acceleration.

Correct A. 2.0 m/s²

B. 3.0 m/s²

C. 2.5 m/s²

D. 1.0 m/s²

Correct Answer: A

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Question 6 View Details

A 2.0‑kg block is placed at the top of a smooth 5.00‑m long incline that makes an angle of 30° with the horizontal. The block is released from rest and slides down, compressing a horizontal spring of spring constant 800 N m⁻¹ fixed at the foot of the incline. The spring is compressed by 0.10 m before the block comes to rest. The kinetic friction coefficient μ_k between the block and the incline is unknown. (a) Determine μ_k. (b) Find the average power delivered by the block to the spring during the compression phase.

A. μ_k = 0.45 (dimensionless); average power ≈ 1.20×10^2 W

B. μ_k = 0.60 (dimensionless); average power ≈ 1.50×10^2 W

Correct C. μ_k = 0.53 (dimensionless); average power ≈ 1.34×10^2 W

D. μ_k = 0.38 (dimensionless); average power ≈ 1.05×10^2 W

Correct Answer: C

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Question 7 View Details

A string 1.20 m long is fixed at both ends and vibrates in its third harmonic with a frequency of 180 Hz. The linear mass density of the string is 0.025 kg m⁻¹. (a) Calculate the speed of the transverse wave on the string and the tension in the string. (b) If the tension is increased by 20 % while the string length remains unchanged, what is the new frequency of the third harmonic.

Correct A. Wave speed = 144 m/s; tension = 5.18×10² N; new frequency ≈ 197 Hz

B. Wave speed = 130 m\/s; tension = 4.70×10² N; new frequency ≈ 185 Hz

C. Wave speed = 120 m\/s; tension = 3.90×10² N; new frequency ≈ 170 Hz

D. Wave speed = 158 m\/s; tension = 5.80×10² N; new frequency ≈ 210 Hz

Correct Answer: A

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Question 8 View Details

A 150 g iron block (specific heat 0.45 J g⁻¹ °C⁻¹) initially at 200 °C is immersed in 200 g of water (specific heat 4.18 J g⁻¹ °C⁻¹) at 25 °C in an insulated container. (a) Find the equilibrium temperature of the system. (b) To raise the temperature of the mixture to 80 °C, steam at 100 °C is introduced and allowed to condense completely. Assuming the latent heat of vaporisation of water is 2260 J g⁻¹ and the specific heat of liquid water is 4.18 J g⁻¹ °C⁻¹, calculate the mass of steam required.

A. Equilibrium temperature ≈ 30.8 °C; steam required ≈ 20.3 g

B. Equilibrium temperature ≈ 35.0 °C; steam required ≈ 18.5 g

Correct C. Equilibrium temperature ≈ 38.1 °C; steam required ≈ 16.2 g

D. Equilibrium temperature ≈ 41.2 °C; steam required ≈ 12.9 g

Correct Answer: C

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Question 9 View Details

Two point charges are placed on the y‑axis: a +8 µC charge at the origin O and a -2 µC charge at point A (0, 0.12 m). (a) Determine the magnitude and direction of the net electric field at point P (0.08 m, 0). (b) A test charge of +1 µC is moved from P to point Q (0, 0.20 m) along a straight line. Calculate the work done by the electric field on the test charge during this displacement. (c) Find the electric potential difference V_P - V_Q.

A. E ≈ 1.15×10⁷ N C⁻¹ at 2.1° above +x; work = 0.72 J; V_P‑V_Q = 6.90×10⁵ V

B. E ≈ 9.5×10⁶ N C⁻¹ at 5.2° above +x; work = 0.55 J; V_P‑V_Q = 5.80×10⁵ V

Correct C. E ≈ 1.08×10⁷ N C⁻¹ at 3.8° above +x; work = 0.64 J; V_P‑V_Q = 6.40×10⁵ V

D. E ≈ 1.02×10⁷ N C⁻¹ at 4.5° above +x; work = 0.60 J; V_P‑V_Q = 6.20×10⁵ V

Correct Answer: C

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Question 10 View Details

A 2.0‑mol sample of an ideal gas initially at 300 K and 1.00 atm occupies 24.0 L. The gas is heated at constant pressure, absorbing 1746 J of heat and doing 500 J of work on the surroundings. The molar heat capacity at constant pressure is C_p = 29.1 J mol⁻¹ K⁻¹. (a) Determine the final temperature of the gas and the change in its internal energy. (b) What is the final pressure of the gas after heating?

A. T_f = 320 K; ΔU = +1.10×10³ J; final pressure ≈ 1.78 atm

Correct B. T_f = 330 K; ΔU = +1.25×10³ J; final pressure ≈ 1.87 atm

C. T_f = 330 K; ΔU = +1.00×10³ J; final pressure ≈ 1.87 atm

D. T_f = 340 K; ΔU = +1.30×10³ J; final pressure ≈ 1.95 atm

Correct Answer: B

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Question 11 View Details

A car travels 60 km north and then 80 km east. What is the magnitude of its displacement from the starting point?

A. 140 km

Correct B. 100 km

C. 80 km

D. 120 km

Correct Answer: B

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Question 12 View Details

A converging lens forms a real image of a candle on a screen. The distance between the candle and the screen is 120 cm. The image is twice the size of the candle. Find the focal length of the lens (in cm).

A. 24.0 cm

Correct B. 26.7 cm

C. 20.0 cm

D. 30.0 cm

Correct Answer: B

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Question 13 View Details

A metal rod has a length of 2.00 m at 20°C. When heated to 120°C, its length becomes 2.04 m. Determine the coefficient of linear expansion $\alpha$ of the metal in per °C.

A. 1.5×10⁻⁴ °C⁻¹

B. 2.5×10⁻⁴ °C⁻¹

C. 3.0×10⁻⁴ °C⁻¹

Correct D. 2.0×10⁻⁴ °C⁻¹

Correct Answer: D

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Question 14 View Details

A sealed container holds 2.0 L of an ideal gas at 1.0 atm and 300 K. The container is then immersed in water where the external water pressure is 3.0×10⁵ Pa. Assuming the temperature remains constant, what is the new volume of the gas? (Take 1 atm = 1.013×10⁵ Pa.)

A. 0.85 L

B. 0.68 L

Correct C. 0.51 L

D. 0.34 L

Correct Answer: C

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Question 15 View Details

A block‑and‑tackle system is used to lift a load of 500 N. The effort applied is 150 N. While the load is raised by 0.30 m, the point of application of the effort moves through 0.90 m. Determine (a) the ideal mechanical advantage (IMA), (b) the actual mechanical advantage (AMA), and (c) the efficiency of the system as a percentage.

A. IMA = 3.00, AMA = 3.33, efficiency = 90%

B. IMA = 3.33, AMA = 2.78, efficiency = 84%

C. IMA = 3.33, AMA = 3.00, efficiency = 80%

Correct D. IMA = 3.33, AMA = 3.00, efficiency = 90%

Correct Answer: D

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Question 16 View Details

A 150 g block of an unknown metal at 120 °C is placed into 200 g of water at 25 °C in an insulated container. The system reaches a final equilibrium temperature of 30 °C. During the process the metal oxidises, losing 5 % of its mass; each gram of metal lost releases 10 J of heat. Assuming no heat loss to the surroundings, determine the specific heat capacity of the metal in J kg⁻¹ K⁻¹.

A. 3.05×10^3

B. 2.95×10^2

C. 3.15×10^2

Correct D. 3.05×10^2

Correct Answer: D

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Question 17 View Details

A source emits a sound of frequency 800 Hz in air. An observer moves directly towards the stationary source with a speed of 30 m s⁻¹ and measures the frequency as 860 Hz. The speed of sound in air varies with temperature according to v = 331 + 0.6 T (where T is in °C). Determine the air temperature.

A. 130

B. 125

Correct C. 115

D. 105

Correct Answer: C

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Question 18 View Details

A 2.0 kg block is released from rest at the top of a rough inclined plane 10.0 m long that makes an angle of 30° with the horizontal. The coefficient of kinetic friction between the block and the plane is 0.20. At the bottom of the incline the block compresses a horizontal spring of spring constant 500 N m⁻¹ and comes to rest after compressing it by a distance x. Find x (in metres).

Correct A. 0.51

B. 0.60

C. 0.45

D. 0.73

Correct Answer: A

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Question 19 View Details

A loudspeaker emits sound uniformly in air. At a distance of 5 m from the speaker the intensity level is measured as 90 dB. The atmospheric absorption coefficient for the sound is 0.005 dB m⁻¹. Assuming spherical spreading of the sound, determine the intensity level (in dB, to one decimal place) at a distance of 20 m from the speaker, taking both spherical spreading and atmospheric absorption into account.

A. 73.5

B. 71.0

Correct C. 77.9

D. 80.2

Correct Answer: C

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Question 20 View Details

A string of length 0.80 m is fixed at both ends. Its linear mass density is initially 0.010 kg m⁻¹ and the tension in the string is such that its fundamental frequency is 120 Hz. The tension is then increased by 20 % while the length remains unchanged. Under the new tension the frequency of the third harmonic is measured to be 540 Hz. Determine the new linear mass density of the string (in kg m⁻¹, expressed to three significant figures).

A. 6.12×10^-3

B. 4.27×10^-3

C. 5.33×10^-2

Correct D. 5.33×10^-3

Correct Answer: D

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Question 21 View Details

A battery of unknown emf E and internal resistance r is connected to a load resistor. When a 10 Ω resistor is connected, the terminal voltage is 6 V. When a 20 Ω resistor is connected, the terminal voltage is 8 V. Determine (i) the emf and internal resistance of the battery, (ii) the value of external resistance that will make the power delivered to the load maximum, and (iii) the maximum power transferred to the load.

Correct A. E = 12 V; r = 10 Ω; R = 10 Ω; Pmax = 3.6 W

B. E = 10 V; r = 12 Ω; R = 12 Ω; Pmax = 2.5 W

C. E = 14 V; r = 8 Ω; R = 8 Ω; Pmax = 4.9 W

D. E = 12 V; r = 8 Ω; R = 8 Ω; Pmax = 4.8 W

Correct Answer: A

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Question 22 View Details

Two point charges are placed on the x‑axis. A charge +8 µC is at the origin and a charge -2 µC is at x = 0.30 m. (a) Find the position on the x‑axis where the net electric field is zero. (b) A test charge +1 µC is placed at that point and moved to the point x = 0.50 m. Calculate the work done by the electric field during this displacement.

Correct A. 0.126 J

B. 0.210 J

C. 0.158 J

D. 0.094 J

Correct Answer: A

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Question 23 View Details

A block‑and‑tackle system consists of two fixed pulleys and one movable pulley, giving an ideal mechanical advantage of 3. An effort of 200 N moves the effort rope through 0.90 m while the load (500 N) rises 0.25 m. Determine (i) the actual mechanical advantage, (ii) the efficiency of the system, and (iii) the magnitude of the constant friction force acting in the system.

A. MA = 2.3; Efficiency = 65.2%; Friction force = 68.4 N

B. MA = 3.0; Efficiency = 60.0%; Friction force = 70.0 N

C. MA = 2.8; Efficiency = 72.0%; Friction force = 55.0 N

Correct D. MA = 2.5; Efficiency = 69.4%; Friction force = 61.1 N

Correct Answer: D

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Question 24 View Details

A car starts from rest, accelerates uniformly to 20 m·s⁻¹ in 5 s, then travels at this constant speed for 30 s, and finally decelerates uniformly to rest in 4 s. Find the total distance covered by the car during the whole motion.

Correct A. 690 m

B. 720 m

C. 650 m

D. 600 m

Correct Answer: A

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Question 25 View Details

A copper wire of length 2.0 m and cross‑sectional area $1.0\,\text{mm}^2$ has a resistivity of $1.68\times10^{-8}\,\Omega\,\text{m}$ at $20^{\circ}\text{C}$. Its temperature coefficient of resistance is $0.004\,\text{°C}^{-1}$. The wire is used as a heating element and is allowed to reach $120^{\circ}\text{C}$. Determine (i) the resistance of the wire at $120^{\circ}\text{C}$, (ii) the current that will cause it to dissipate $100\,\text{W}$ at that temperature, and (iii) the voltage across the wire at that current.

A. R = 0.050 Ω; I = 44.7 A; V = 2.24 V

B. R = 0.048 Ω; I = 45.6 A; V = 2.19 V

C. R = 0.034 Ω; I = 54.5 A; V = 1.85 V

Correct D. R = 0.047 Ω; I = 46.1 A; V = 2.17 V

Correct Answer: D

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