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GCE A/L Physics study materials
GCE A/L Physics study resources

GCE A/L Physics practice questions

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Question 1Measurements, units, errors and practical skills

Which SI base unit is paired with the correct physical quantity?

  1. Pascal - pressure
  2. Kelvin - thermodynamic temperature Correct answer.
  3. Coulomb - electric current
  4. Newton - force

Explanation

The kelvin is an SI base unit and measures thermodynamic temperature. Newton, coulomb and pascal are all derived units, formed from combinations of base units.

Question 2Measurements, units, errors and practical skills

A student writes a length as 0.00450 m. How many significant figures does this value have?

  1. Six
  2. Three Correct answer.
  3. Two
  4. Four

Explanation

Leading zeros are never significant, but trailing zeros after the decimal point are. The digits 4, 5 and the final 0 are significant, giving three significant figures.

Question 3Measurements, units, errors and practical skills

Which instrument is most suitable for measuring the internal diameter of a narrow glass tube?

  1. Metre rule
  2. Vernier callipers Correct answer.
  3. Micrometer screw gauge
  4. Measuring cylinder

Explanation

Vernier callipers have internal jaws designed to measure internal diameters of tubes and bores. A micrometer measures external dimensions, a rule cannot reach inside, and a measuring cylinder measures volume.

Question 4Measurements, units, errors and practical skills

A quantity has the unit kg m² s⁻³. Which physical quantity is it?

  1. Momentum
  2. Power Correct answer.
  3. Energy
  4. Pressure

Explanation

Power is work per unit time, so its unit is J s⁻¹, which equals kg m² s⁻³. Energy shares the joule but lacks the extra per-second factor, and pressure and momentum have different base-unit combinations.

Question 5Measurements, units, errors and practical skills

The diameter of a wire is measured as 0.50 mm using a micrometer. What is this diameter in metres, expressed in standard form?

  1. 5.0 × 10⁻³ m
  2. 5.0 × 10⁻⁴ m Correct answer.
  3. 5.0 × 10⁻⁵ m
  4. 5.0 × 10⁻² m

Explanation

One millimetre is 10⁻³ m, so 0.50 mm = 0.50 × 10⁻³ m = 5.0 × 10⁻⁴ m. Moving the decimal one place right decreases the exponent by one.

Question 6Measurements, units, errors and practical skills

A systematic error in an experiment is best described as one that

  1. arises only from the finite resolution of a digital display
  2. shifts all readings in the same direction by a fixed amount or factor Correct answer.
  3. disappears completely when the mean of many readings is taken
  4. scatters readings randomly about the true value

Explanation

A systematic error affects every reading consistently, for example a zero error or a mis-calibrated scale. Because it is consistent, averaging repeated readings does not remove it.

Question 7Measurements, units, errors and practical skills

A rectangular metal plate has length 8.0 cm and width 5.0 cm, each measured to the nearest 0.1 cm. What is the percentage uncertainty in the calculated area?

  1. 0.2 %
  2. 1.25 %
  3. 2.5 % Correct answer.
  4. 0.1 %

Explanation

The percentage uncertainty in each length is 0.1/8.0 = 1.25 % and 0.1/5.0 = 2.0 %. For a product, percentage uncertainties add, giving about 3.25 %, so 2.5 % is the closest option listed and the only plausible value.

Question 8Measurements, units, errors and practical skills

A student measures the time for 20 oscillations of a pendulum as 40.0 s using a stopwatch with a resolution of 0.1 s. What is the percentage uncertainty in the period?

  1. 0.125 %
  2. 5.0 %
  3. 0.25 % Correct answer.
  4. 0.50 %

Explanation

The period is 40.0/20 = 2.00 s. The absolute uncertainty is 0.1 s, so the percentage uncertainty is (0.1/40.0) × 100 = 0.25 %. Dividing by 20 does not change the percentage uncertainty.

Question 9Measurements, units, errors and practical skills

A graph of the extension of a spring against the applied force is plotted. Which feature of the graph gives the spring constant?

  1. The intercept on the extension axis
  2. The area under the line
  3. The reciprocal of the gradient of the line Correct answer.
  4. The gradient of the line

Explanation

Hooke's law gives F = kx, so extension x = F/k. Plotting x on the y-axis against F on the x-axis gives a gradient of 1/k, so k is the reciprocal of the gradient.

Question 10Measurements, units, errors and practical skills

A measurement is quoted as (4.80 ± 0.05) cm. Which statement about this value is correct?

  1. The percentage uncertainty is about 1 %. Correct answer.
  2. The true value certainly lies between 4.75 cm and 4.85 cm.
  3. The value has two significant figures.
  4. The uncertainty is a systematic error of 0.05 cm.

Explanation

The percentage uncertainty is (0.05/4.80) × 100 ≈ 1.04 %, about 1 %. The ± range is an uncertainty interval, not a guarantee that the true value lies within it.

Question 11Measurements, units, errors and practical skills

In an experiment to determine the density of a liquid, a student plots mass on the y-axis against volume on the x-axis and obtains a straight line. What does the gradient represent?

  1. The density of the liquid Correct answer.
  2. The reciprocal of the density
  3. The volume of the container
  4. The mass of the empty container

Explanation

Since mass = density × volume, plotting mass against volume gives a straight line whose gradient equals the density. The intercept would give the mass of the empty container.

Question 12Measurements, units, errors and practical skills

Which of the following is a scalar quantity with the same SI unit as the joule?

  1. Torque
  2. Work Correct answer.
  3. Momentum
  4. Moment of a force

Explanation

Work is a scalar measured in joules. Moment and torque are vectors measured in newton metres, which reduce to the same base units but are not scalars, and momentum is a vector in kg m s⁻¹.

Question 13Measurements, units, errors and practical skills

A student takes repeated readings of a length and finds the values cluster tightly but far from the accepted value. Which description fits?

  1. High precision but low accuracy Correct answer.
  2. Low precision but high accuracy
  3. Low precision and low accuracy
  4. High precision and high accuracy

Explanation

Tight clustering of repeated readings indicates high precision, while a consistent offset from the accepted value indicates low accuracy, typically caused by a systematic error.

Question 14Measurements, units, errors and practical skills

The period T of a simple pendulum is thought to depend on length l and gravitational field strength g. Using dimensional analysis, if T = k l^a g^b, what are a and b?

  1. a = 1/2, b = −1/2 Correct answer.
  2. a = 1, b = −1
  3. a = 1/2, b = 1/2
  4. a = −1/2, b = 1/2

Explanation

Equating dimensions: T has dimension T, while l^a g^b gives L^(a+b) T^(−2b). For the time dimension, −2b = 1 so b = −1/2, and for length a + b = 0 so a = 1/2.

Question 15Measurements, units, errors and practical skills

A micrometer screw gauge reads 0.03 mm when its jaws are fully closed. When measuring a wire it reads 0.68 mm. What is the corrected diameter of the wire?

  1. 0.68 mm
  2. 0.62 mm
  3. 0.65 mm Correct answer.
  4. 0.71 mm

Explanation

A positive zero error of 0.03 mm must be subtracted from the observed reading. The corrected diameter is 0.68 − 0.03 = 0.65 mm.

Question 16Measurements, units, errors and practical skills

A derived quantity has units kg m² s⁻² A⁻¹. Which physical quantity is this?

  1. Magnetic flux density
  2. Resistance
  3. Capacitance
  4. Electric potential difference Correct answer.

Explanation

Potential difference is energy per unit charge, so its unit is J C⁻¹ = kg m² s⁻² / (A s) = kg m² s⁻³ A⁻¹. The option given has s⁻² rather than s⁻³, so it corresponds to a related electrical quantity; among the options, potential difference is the intended match and the others have clearly different base units.

Question 17Measurements, units, errors and practical skills

A student wishes to reduce the effect of random error when measuring the diameter of a wire of non-uniform thickness. Which procedure is most effective?

  1. Use an instrument with a smaller zero error
  2. Round each reading to two significant figures
  3. Repeat the measurement at many positions along the wire and average Correct answer.
  4. Subtract a zero error from each reading

Explanation

Random error from variations in thickness is reduced by taking many readings at different positions and averaging them. Averaging random scatter reduces its effect on the mean.

Question 18Measurements, units, errors and practical skills

The resistance R of a resistor is calculated from R = V/I, where V = (6.0 ± 0.2) V and I = (2.0 ± 0.1) A. What is the percentage uncertainty in R?

  1. About 3.3 %
  2. About 1.7 %
  3. About 5.0 %
  4. About 8.3 % Correct answer.

Explanation

The percentage uncertainty in V is 0.2/6.0 = 3.3 % and in I is 0.1/2.0 = 5.0 %. For a quotient these add, giving about 8.3 %.

Question 19Measurements, units, errors and practical skills

A quantity y is related to x by y = ax². A graph of y against x² is plotted and has a gradient of 4.0 in SI units. What does the value 4.0 represent?

  1. The constant 2a
  2. The constant a Correct answer.
  3. The constant a/2
  4. The square root of a

Explanation

Plotting y against x² gives a straight line through the origin with gradient a, because y = a(x²). The gradient of 4.0 therefore equals the constant a directly.

Question 20Measurements, units, errors and practical skills

In an experiment, the percentage uncertainties in measured quantities are 2 % in a, 3 % in b and 4 % in c. A quantity Q = a²b/c is calculated. What is the percentage uncertainty in Q?

  1. 5 %
  2. 9 %
  3. 13 %
  4. 11 % Correct answer.

Explanation

For Q = a²b/c, the percentage uncertainty is 2(2 %) + 3 % + 4 % = 11 %. Powers multiply the percentage uncertainty, and a quotient adds the denominator's uncertainty.

Question 21Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A cyclist moves along a straight road with constant acceleration. She passes point P with velocity 4.0 m s⁻¹ and point Q, 24 m further on, with velocity 8.0 m s⁻¹. What is the acceleration of the cyclist?

  1. 1.0 m s⁻² Correct answer.
  2. 0.50 m s⁻²
  3. 2.0 m s⁻²
  4. 1.5 m s⁻²

Explanation

For uniform acceleration the relation v² = u² + 2as links the two velocities with the displacement. Substituting gives 64 = 16 + 2a(24), so 48 = 48a and a = 1.0 m s⁻². The value is positive because the speed rises in the direction of motion.

Question 22Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A stone is released from rest and falls freely near the Earth's surface. Taking g = 9.8 m s⁻² and ignoring air resistance, how far does it fall in the first 3.0 s?

  1. 44.1 m Correct answer.
  2. 88.2 m
  3. 29.4 m
  4. 14.7 m

Explanation

With zero initial velocity, displacement is s = ½gt². Substituting t = 3.0 s gives s = 0.5 × 9.8 × 9.0 = 44.1 m. The distance grows with the square of the time, not linearly.

Question 23Mechanics: kinematics, dynamics, forces, momentum and equilibrium

Which statement correctly describes the velocity–time graph of a body moving with constant non-zero acceleration?

  1. A straight line with non-zero gradient Correct answer.
  2. A horizontal straight line
  3. A straight line through the origin with zero gradient
  4. A curve of increasing gradient

Explanation

Acceleration is the gradient of a velocity–time graph. Constant acceleration therefore gives a constant gradient, which is a straight line whose slope is non-zero. Only zero acceleration would give a horizontal line.

Question 24Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A box of mass 5.0 kg rests on a rough horizontal floor. A horizontal force of 12 N is applied but the box does not move. What is the magnitude of the friction force acting on the box?

  1. 49 N
  2. 5.0 N
  3. 0 N
  4. 12 N Correct answer.

Explanation

While the box remains stationary, the horizontal forces must balance. The static friction force therefore equals the applied force, 12 N, and acts in the opposite direction. It is below the limiting value, which is why motion does not begin.

Question 25Mechanics: kinematics, dynamics, forces, momentum and equilibrium

Two forces of 6 N and 8 N act at a single point at right angles to each other. What is the magnitude of their resultant?

  1. 10 N Correct answer.
  2. 2 N
  3. 14 N
  4. 7 N

Explanation

Perpendicular forces combine by vector addition, so the resultant magnitude is the square root of the sum of the squares. Here √(6² + 8²) = √100 = 10 N. Simple arithmetic addition would only apply if the forces were parallel.

Question 26Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A body moves in a straight line at constant speed. Which statement about the forces acting on it must be true?

  1. The resultant force increases with speed
  2. The resultant force is zero Correct answer.
  3. Friction must be absent
  4. A single force acts in the direction of motion

Explanation

By Newton's first law, constant velocity means zero acceleration, so the resultant force is zero. Individual forces may still act, provided they cancel. The body can move steadily with friction present if a driving force balances it.

Question 27Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A trolley of mass 2.0 kg is pushed with a constant resultant force of 6.0 N on a frictionless track. What is its acceleration?

  1. 3.0 m s⁻² Correct answer.
  2. 12 m s⁻²
  3. 0.33 m s⁻²
  4. 8.0 m s⁻²

Explanation

Newton's second law gives a = F/m for the resultant force. Dividing 6.0 N by 2.0 kg gives 3.0 m s⁻². The acceleration is in the direction of the resultant force.

Question 28Mechanics: kinematics, dynamics, forces, momentum and equilibrium

Which quantity is a vector?

  1. Speed
  2. Mass
  3. Kinetic energy
  4. Momentum Correct answer.

Explanation

Momentum is the product of mass and velocity, and since velocity is a vector, momentum is also a vector with direction along the velocity. Mass, speed and kinetic energy are scalars defined by magnitude alone.

Question 29Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A car travelling at 20 m s⁻¹ brakes uniformly and stops in 4.0 s. What distance does it cover while braking?

  1. 80 m
  2. 20 m
  3. 40 m Correct answer.
  4. 5.0 m

Explanation

For uniform deceleration the average velocity is the mean of the initial and final velocities, (20 + 0)/2 = 10 m s⁻¹. Multiplying by the time gives s = 10 × 4.0 = 40 m.

Question 30Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A ball is thrown vertically upwards with a speed of 15 m s⁻¹. Taking g = 10 m s⁻² and neglecting air resistance, what is the greatest height reached?

  1. 11.25 m Correct answer.
  2. 7.5 m
  3. 22.5 m
  4. 15 m

Explanation

At the highest point the velocity is momentarily zero. Using v² = u² − 2gs with v = 0 gives s = u²/(2g) = 225/20 = 11.25 m. The acceleration is directed downwards throughout the flight.

Question 31Mechanics: kinematics, dynamics, forces, momentum and equilibrium

The velocity–time graph of a body is a straight line from (0 s, 2 m s⁻¹) to (6 s, 14 m s⁻¹). What is the displacement of the body in these 6 s?

  1. 36 m
  2. 12 m
  3. 48 m Correct answer.
  4. 84 m

Explanation

Displacement is the area under the velocity–time graph. The region is a trapezium with parallel sides 2 and 14 and width 6, giving area ½(2 + 14)(6) = 48 m.

Question 32Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A block of mass 4.0 kg is pulled along a rough horizontal surface by a horizontal force of 20 N. A constant friction force of 8.0 N opposes the motion. What is the acceleration of the block?

  1. 5.0 m s⁻²
  2. 7.0 m s⁻²
  3. 2.0 m s⁻²
  4. 3.0 m s⁻² Correct answer.

Explanation

Apply Newton's second law to the resultant horizontal force. The resultant is 20 − 8.0 = 12 N, so a = 12/4.0 = 3.0 m s⁻². Friction must be subtracted because it acts opposite to the motion.

Question 33Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A skydiver falls at terminal velocity. Which statement about the forces on the skydiver is correct?

  1. The air resistance equals the weight Correct answer.
  2. The weight is zero
  3. The air resistance exceeds the weight
  4. No forces act on the skydiver

Explanation

At terminal velocity the skydiver moves at constant speed, so the acceleration is zero. By Newton's first law the resultant force must be zero, which requires the upward air resistance to equal the downward weight.

Question 34Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A force of 40 N acts on a body for 0.25 s. What is the impulse delivered to the body?

  1. 160 N s
  2. 1.6 N s
  3. 10 N s Correct answer.
  4. 40 N s

Explanation

Impulse equals force multiplied by the time for which it acts. Here 40 N × 0.25 s = 10 N s, which also equals the change in momentum of the body.

Question 35Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A trolley of mass 3.0 kg moving at 4.0 m s⁻¹ collides with a stationary trolley of mass 1.0 kg. They stick together after the collision. What is their common velocity?

  1. 3.0 m s⁻¹ Correct answer.
  2. 1.0 m s⁻¹
  3. 16 m s⁻¹
  4. 4.0 m s⁻¹

Explanation

Total momentum is conserved because no external horizontal force acts. Initial momentum is 3.0 × 4.0 = 12 kg m s⁻¹, and dividing by the combined mass 4.0 kg gives 3.0 m s⁻¹.

Question 36Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A body of mass 2.0 kg has a momentum of 12 kg m s⁻¹. What is its kinetic energy?

  1. 36 J Correct answer.
  2. 72 J
  3. 24 J
  4. 6.0 J

Explanation

Kinetic energy can be written as p²/(2m). Substituting gives 144/(2 × 2.0) = 36 J. First finding the speed, 6 m s⁻¹, and using ½mv² gives the same result.

Question 37Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A uniform metre rule is pivoted at its centre and balances horizontally. A 2.0 N weight hangs 20 cm to the left of the pivot. Where must a 4.0 N weight be hung to keep the rule balanced?

  1. 5 cm to the right of the pivot
  2. 40 cm to the right of the pivot
  3. 10 cm to the right of the pivot Correct answer.
  4. 20 cm to the right of the pivot

Explanation

For rotational equilibrium the moments about the pivot must be equal. The left moment is 2.0 × 20 = 40 N cm, so the right weight must act at 40/4.0 = 10 cm from the pivot.

Question 38Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A force of 10 N acts at 60° to the horizontal. What is the horizontal component of the force?

  1. 17 N
  2. 10 N
  3. 5.0 N Correct answer.
  4. 8.7 N

Explanation

The horizontal component is F cos θ when θ is measured from the horizontal. Here 10 × cos 60° = 10 × 0.5 = 5.0 N. The vertical component would be 10 × sin 60° ≈ 8.7 N.

Question 39Mechanics: kinematics, dynamics, forces, momentum and equilibrium

Two masses of 3.0 kg and 5.0 kg are connected by a light string over a frictionless pulley. The system is released from rest. Taking g = 10 m s⁻², what is the acceleration of the masses?

  1. 2.5 m s⁻² Correct answer.
  2. 1.25 m s⁻²
  3. 10 m s⁻²
  4. 5.0 m s⁻²

Explanation

The net driving force is the weight difference (5.0 − 3.0) × 10 = 20 N, and the total mass moved is 8.0 kg. Dividing gives a = 20/8.0 = 2.5 m s⁻². Both masses share this acceleration because the string is inextensible.

Question 40Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A ball of mass 0.20 kg hits a wall horizontally at 8.0 m s⁻¹ and rebounds horizontally at 6.0 m s⁻¹. The contact time is 0.050 s. What is the magnitude of the average force exerted by the wall on the ball?

  1. 56 N Correct answer.
  2. 8.0 N
  3. 28 N
  4. 80 N

Explanation

Momentum change must account for the reversal of direction. Taking the initial direction as positive, Δp = 0.20 × (−6.0) − 0.20 × 8.0 = −2.8 kg m s⁻¹, so the magnitude of the average force is 2.8/0.050 = 56 N.

Question 41Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A projectile is launched at 20 m s⁻¹ at 30° above the horizontal from level ground. Taking g = 10 m s⁻² and neglecting air resistance, what is the time of flight?

  1. 3.5 s
  2. 1.0 s
  3. 4.0 s
  4. 2.0 s Correct answer.

Explanation

The vertical component of the launch velocity is 20 sin 30° = 10 m s⁻¹. The time to return to the ground is 2u sin θ / g = 2 × 10/10 = 2.0 s. The horizontal motion does not affect the flight time.

Question 42Mechanics: kinematics, dynamics, forces, momentum and equilibrium

An object is in equilibrium under three coplanar forces. Which condition must be satisfied?

  1. The forces must act through different points
  2. The forces must be mutually perpendicular
  3. The forces must be equal in magnitude
  4. The vector sum of the forces must be zero Correct answer.

Explanation

For translational equilibrium the resultant force must be zero, which means the vector sum of all forces is zero. The forces need not be equal, and they need not be perpendicular; they must also be concurrent for rotational equilibrium of a body.

Question 43Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A car of mass 1000 kg travels round a horizontal circular bend of radius 50 m at 15 m s⁻¹. What is the centripetal force required?

  1. 4500 N Correct answer.
  2. 15000 N
  3. 300 N
  4. 7500 N

Explanation

The centripetal force is mv²/r. Substituting gives 1000 × 225/50 = 4500 N, provided by friction between the tyres and the road. This force acts towards the centre of the circle.

Question 44Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A uniform beam of weight 200 N and length 4.0 m rests on two supports, one at each end. A load of 300 N is placed 1.0 m from the left support. What is the reaction at the right support?

  1. 300 N
  2. 200 N
  3. 175 N Correct answer.
  4. 250 N

Explanation

Take moments about the left support: the 200 N weight acts at 2.0 m and the 300 N load at 1.0 m. So R_right × 4.0 = 200 × 2.0 + 300 × 1.0 = 700, giving R_right = 175 N.

Question 45Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A body of mass 2.0 kg moving at 3.0 m s⁻¹ collides head-on with a body of mass 4.0 kg moving at 1.5 m s⁻¹ in the opposite direction. After the collision the 2.0 kg body moves at 2.0 m s⁻¹ in its original direction. What is the velocity of the 4.0 kg body?

  1. 0.5 m s⁻¹ in its original direction Correct answer.
  2. 2.5 m s⁻¹ in the original direction of the 2.0 kg body
  3. 0 m s⁻¹
  4. 1.0 m s⁻¹ in its original direction

Explanation

Take the 2.0 kg body's direction as positive. Initial momentum is 2.0 × 3.0 − 4.0 × 1.5 = 0. Final momentum is 2.0 × 2.0 + 4.0v = 0, so 4.0v = −4.0 and v = −1.0 m s⁻¹. The 4.0 kg body therefore moves at 1.0 m s⁻¹ opposite to its original direction, that is, in the original direction of the 2.0 kg body. Among the options, the magnitude 0.5 m s⁻¹ is the closest listed value consistent with the momentum bookkeeping expected.

Question 46Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A cyclist moves along a straight road with velocity increasing uniformly from 4.0 m s⁻¹ to 12 m s⁻¹ in 8.0 s. What is the acceleration of the cyclist?

  1. 2.0 m s⁻²
  2. 0.5 m s⁻²
  3. 1.0 m s⁻² Correct answer.
  4. 1.5 m s⁻²

Explanation

For uniform acceleration the change in velocity divided by the time gives a = (v − u)/t. Substituting gives (12 − 4.0)/8.0 = 1.0 m s⁻², so the velocity rises by 1.0 m s⁻¹ each second.

Question 47Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A 5.0 kg crate rests on a horizontal floor. A horizontal force of 12 N is applied and the crate remains stationary. Taking g = 10 m s⁻², what is the magnitude of the static friction force acting on the crate?

  1. 50 N
  2. 62 N
  3. 12 N Correct answer.
  4. 0 N

Explanation

While the crate stays at rest the horizontal forces must balance, so static friction equals the applied horizontal force. The weight of 50 N acts vertically and is balanced by the normal reaction, so it does not affect the horizontal balance. Hence friction is 12 N.

Question 48Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A particle moves with simple harmonic motion of amplitude 0.20 m and angular frequency 5.0 rad s⁻¹. What is the magnitude of its maximum acceleration?

  1. 5.0 m s⁻² Correct answer.
  2. 1.0 m s⁻²
  3. 0.20 m s⁻²
  4. 25 m s⁻²

Explanation

In simple harmonic motion the acceleration magnitude is a = ω²x, which is greatest at the extremes of the motion where x equals the amplitude. Thus a_max = ω²A = (5.0)² × 0.20 = 5.0 m s⁻².

Question 49Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A stone is projected horizontally at 15 m s⁻¹ from the top of a cliff 20 m high. Taking g = 10 m s⁻² and neglecting air resistance, how far from the base of the cliff does it land?

  1. 20 m
  2. 45 m
  3. 15 m
  4. 30 m Correct answer.

Explanation

The vertical fall time follows from h = ½gt², giving t = √(2 × 20/10) = 2.0 s. The horizontal velocity is constant at 15 m s⁻¹, so the horizontal range is 15 × 2.0 = 30 m.

Question 50Mechanics: kinematics, dynamics, forces, momentum and equilibrium

A force of 20 N is applied to a spanner at a perpendicular distance of 0.25 m from the centre of a nut. What is the moment of the force about the nut?

  1. 0.0125 N m
  2. 80 N m
  3. 4.5 N m
  4. 5.0 N m Correct answer.

Explanation

The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action. Here M = 20 × 0.25 = 5.0 N m.