I85PREP
⌘ K
MATSEC IM Physics study materials
MATSEC IM Physics study resources

MATSEC IM Physics practice questions

One question at a time. Build your MATSEC IM Physics understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Mechanics and Properties of Matter

A student measures the length of a metal rod as 24.6 cm using a metre rule. Which statement about this measurement is correct?

  1. It has an uncertainty of ±1 cm because the rule is one metre long.
  2. It has no uncertainty because the rule is a standard laboratory instrument.
  3. It has an uncertainty of ±2.46 cm, which is ten per cent of the reading.
  4. It has an uncertainty of about ±0.1 cm because the rule's smallest division is 1 mm. Correct answer.

Explanation

The uncertainty of a single reading on an analogue scale is typically half the smallest division, or at least one division depending on convention; with a 1 mm scale this gives roughly ±0.1 cm. Instrument length does not affect the absolute reading uncertainty.

Question 2Mechanics and Properties of Matter

A quantity has the SI unit kg m s⁻². Which physical quantity is it?

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

Explanation

The newton is defined as the force giving a 1 kg mass an acceleration of 1 m s⁻², so its base units are kg m s⁻². Energy and work have units kg m² s⁻², while pressure adds an extra inverse metre.

Question 3Mechanics and Properties of Matter

A cyclist travels 300 m east in 20 s and then 100 m west in 10 s. What is the average velocity for the whole journey?

  1. 13.3 m s⁻¹ east
  2. 10 m s⁻¹ east
  3. 6.7 m s⁻¹ east Correct answer.
  4. 20 m s⁻¹ east

Explanation

Displacement is 300 − 100 = 200 m east and total time is 30 s, so average velocity is 200/30 ≈ 6.7 m s⁻¹ east. Average speed would instead use the total path length of 400 m.

Question 4Mechanics and Properties of Matter

A ball is dropped from rest and falls freely for 2.0 s. Taking g = 9.8 m s⁻², how far does it fall?

  1. 39.2 m
  2. 4.9 m
  3. 9.8 m
  4. 19.6 m Correct answer.

Explanation

Using s = ut + ½at² with u = 0 gives s = ½ × 9.8 × 2.0² = 19.6 m. The distance grows with the square of the time, so doubling the time quadruples the fall.

Question 5Mechanics and Properties of Matter

Which statement best describes the centre of gravity of a uniform metre rule?

  1. It is the point where the rule's mass is greatest.
  2. It always lies at the end of the rule nearest the pivot.
  3. It lies at the 0 cm mark, where the rule is supported.
  4. It lies at the 50 cm mark, where the weight of the rule may be taken to act. Correct answer.

Explanation

For a uniform rule the mass is evenly distributed, so the centre of gravity coincides with the geometric centre at the 50 cm mark. The entire weight can be modelled as acting at this single point.

Question 6Mechanics and Properties of Matter

A force of 30 N acts on a mass of 6.0 kg on a frictionless surface. What is the acceleration?

  1. 0.20 m s⁻²
  2. 180 m s⁻²
  3. 5.0 m s⁻² Correct answer.
  4. 36 m s⁻²

Explanation

Newton's second law gives a = F/m = 30/6.0 = 5.0 m s⁻². The acceleration is directly proportional to the applied force for a fixed mass.

Question 7Mechanics and Properties of Matter

A spring obeys Hooke's law. If a force of 4.0 N extends it by 8.0 cm, what is its spring constant in N m⁻¹?

  1. 32
  2. 0.5
  3. 50 Correct answer.
  4. 320

Explanation

Hooke's law gives k = F/x, and 8.0 cm is 0.080 m, so k = 4.0/0.080 = 50 N m⁻¹. Converting the extension to metres before dividing is essential for SI units.

Question 8Mechanics and Properties of Matter

Which pair of quantities is a scalar and a vector respectively?

  1. Energy and temperature
  2. Mass and displacement Correct answer.
  3. Velocity and force
  4. Weight and pressure

Explanation

Mass has magnitude only and is a scalar, while displacement has both magnitude and direction and is a vector. The other pairs either list two vectors or two scalars.

Question 9Mechanics and Properties of Matter

A 2.0 kg block slides down a rough incline at constant velocity. Which statement about the forces on the block is correct?

  1. The normal reaction is equal to the full weight of the block.
  2. Friction is greater than the weight component down the slope.
  3. The component of weight along the slope is balanced by friction, giving zero resultant force. Correct answer.
  4. The resultant force acts down the slope to maintain the motion.

Explanation

Constant velocity means zero acceleration and therefore zero resultant force along the slope. The downhill weight component is exactly cancelled by friction, and the normal reaction balances only the perpendicular weight component.

Question 10Mechanics and Properties of Matter

A rubber ball of mass 0.20 kg hits a wall horizontally at 6.0 m s⁻¹ and rebounds at 4.0 m s⁻¹. What is the magnitude of the change in momentum?

  1. 0.40 kg m s⁻¹
  2. 10 kg m s⁻¹
  3. 2.0 kg m s⁻¹ Correct answer.
  4. 0.80 kg m s⁻¹

Explanation

Taking the initial direction as positive, the change in momentum is m(v − u) = 0.20 × (−4.0 − 6.0) = −2.0 kg m s⁻¹, so the magnitude is 2.0 kg m s⁻¹. Reversal of direction must be handled with signs.

Question 11Mechanics and Properties of Matter

Two skaters at rest push apart on frictionless ice. Skater A has mass 60 kg and moves at 1.5 m s⁻¹. What is the speed of skater B, of mass 45 kg?

  1. 0.75 m s⁻¹
  2. 2.0 m s⁻¹ Correct answer.
  3. 1.1 m s⁻¹
  4. 1.5 m s⁻¹

Explanation

By conservation of momentum, 60 × 1.5 = 45 × v, giving v = 2.0 m s⁻¹. The lighter skater moves faster so that the total momentum remains zero.

Question 12Mechanics and Properties of Matter

A car of mass 1200 kg accelerates uniformly from rest to 20 m s⁻¹ in 8.0 s. What is the average useful power developed?

  1. 240 kW
  2. 2.4 kW
  3. 30 kW Correct answer.
  4. 60 kW

Explanation

Work done equals the gain in kinetic energy, ½ × 1200 × 20² = 240 000 J. Power is energy per time, 240 000/8.0 = 30 000 W, or 30 kW.

Question 13Mechanics and Properties of Matter

A uniform beam of weight 200 N is pivoted at one end and held horizontally by a vertical force at the other end, 2.0 m from the pivot. The beam's weight acts 1.0 m from the pivot. What is the minimum vertical force needed?

  1. 50 N
  2. 400 N
  3. 100 N Correct answer.
  4. 200 N

Explanation

For rotational equilibrium the clockwise moments equal the anticlockwise moments: F × 2.0 = 200 × 1.0. Solving gives F = 100 N, half the weight because the force acts at twice the distance.

Question 14Mechanics and Properties of Matter

A hydraulic press has a small piston of area 5.0 cm² and a large piston of area 200 cm². A force of 40 N is applied to the small piston. What force is produced on the large piston?

  1. 1600 N Correct answer.
  2. 8.0 N
  3. 1000 N
  4. 40 N

Explanation

Pascal's principle states that pressure is transmitted equally, so F₂ = F₁ × A₂/A₁ = 40 × 200/5.0 = 1600 N. The force is multiplied by the ratio of the areas.

Question 15Mechanics and Properties of Matter

A body floats in equilibrium with 40 per cent of its volume submerged in water. What is the density of the body?

  1. 1000 kg m⁻³
  2. 2500 kg m⁻³
  3. 600 kg m⁻³
  4. 400 kg m⁻³ Correct answer.

Explanation

For a floating body the weight equals the weight of displaced fluid, so the body's density is 0.40 times that of water. This gives 0.40 × 1000 = 400 kg m⁻³.

Question 16Mechanics and Properties of Matter

A liquid of density 800 kg m⁻³ fills a tank to a depth of 2.5 m. Taking g = 9.8 m s⁻², what is the gauge pressure at the bottom?

  1. 2.0 kPa
  2. 8.0 kPa
  3. 24.5 kPa
  4. 19.6 kPa Correct answer.

Explanation

Hydrostatic pressure is p = ρgh = 800 × 9.8 × 2.5 ≈ 19 600 Pa, or about 19.6 kPa. Gauge pressure depends only on depth, density and g, not on the tank's shape.

Question 17Mechanics and Properties of Matter

A wire of length 2.0 m and cross-sectional area 1.0 × 10⁻⁶ m² stretches by 1.0 mm under a load of 100 N. What is the Young modulus of the material?

  1. 2.0 × 10¹¹ Pa Correct answer.
  2. 1.0 × 10¹¹ Pa
  3. 5.0 × 10⁻⁶ Pa
  4. 2.0 × 10⁸ Pa

Explanation

Stress is F/A = 100/1.0 × 10⁻⁶ = 1.0 × 10⁸ Pa and strain is 1.0 × 10⁻³/2.0 = 5.0 × 10⁻⁴. Dividing stress by strain gives 2.0 × 10¹¹ Pa.

Question 18Mechanics and Properties of Matter

A body moves in a horizontal circle at constant speed. Which statement about its motion is correct?

  1. It has zero acceleration because its speed is constant.
  2. It accelerates tangentially because it is moving along a curved path.
  3. It experiences no resultant force because the speed does not change.
  4. It accelerates towards the centre because its velocity direction changes continuously. Correct answer.

Explanation

Velocity is a vector, so a change in direction is a change in velocity and therefore an acceleration. This centripetal acceleration points towards the centre and requires a centripetal force.

Question 19Mechanics and Properties of Matter

A stone is whirled in a vertical circle on a string. At the highest point, which force provides the centripetal acceleration?

  1. The weight plus the tension in the string acting downwards Correct answer.
  2. The weight alone acting upwards
  3. The centrifugal force acting outwards
  4. The tension alone acting upwards

Explanation

At the top of the circle both the weight and the string tension point towards the centre, so together they provide the required centripetal force. The minimum speed for the string to stay taut occurs when tension just becomes zero.

Question 20Mechanics and Properties of Matter

A projectile is launched at 20 m s⁻¹ at 30° above the horizontal on level ground. Taking g = 9.8 m s⁻² and neglecting air resistance, what is its horizontal range?

  1. 20 m
  2. 35 m Correct answer.
  3. 70 m
  4. 41 m

Explanation

The range is R = u² sin 2θ / g = 400 × sin 60° / 9.8 ≈ 35 m. The horizontal and vertical motions can be treated independently, with constant horizontal velocity.

Question 21Mechanics and Properties of Matter

A block of mass 3.0 kg is pulled up a rough slope of angle 20° at constant speed by a force parallel to the slope. The friction force is 6.0 N. Taking g = 9.8 m s⁻², what is the pulling force?

  1. 16 N Correct answer.
  2. 6.0 N
  3. 29 N
  4. 10 N

Explanation

At constant speed the pulling force balances both the downhill weight component mg sin 20° ≈ 10 N and friction of 6.0 N, giving about 16 N. The normal reaction does not enter the force balance along the slope.

Question 22Mechanics and Properties of Matter

A uniform metre rule is balanced at its centre. A 40 g mass is hung at the 20 cm mark. Where must a 50 g mass be hung to balance the rule?

  1. At the 26 cm mark
  2. At the 66 cm mark
  3. At the 84 cm mark
  4. At the 74 cm mark Correct answer.

Explanation

Taking moments about the 50 cm pivot: 40 × 30 = 50 × d, so d = 24 cm from the pivot. Placing this on the opposite side gives the 50 + 24 = 74 cm mark.

Question 23Mechanics and Properties of Matter

A spring of force constant 200 N m⁻¹ is compressed by 0.10 m and launches a 0.050 kg ball horizontally on a frictionless surface. What is the ball's speed?

  1. 0.63 m s⁻¹
  2. 20 m s⁻¹
  3. 2.0 m s⁻¹
  4. 6.3 m s⁻¹ Correct answer.

Explanation

The stored elastic energy is ½kx² = ½ × 200 × 0.10² = 1.0 J, and this becomes kinetic energy ½mv². Solving gives v = √(2 × 1.0/0.050) ≈ 6.3 m s⁻¹.

Question 24Mechanics and Properties of Matter

Two forces of 6.0 N and 8.0 N act at a point at right angles to each other. What is the magnitude of their resultant?

  1. 48 N
  2. 2.0 N
  3. 10 N Correct answer.
  4. 14 N

Explanation

Perpendicular forces combine by vector addition, so the resultant magnitude is √(6.0² + 8.0²) = √100 = 10 N. This is a 3-4-5 triangle scaled by two.

Question 25Mechanics and Properties of Matter

A student measures the diameter of a wire five times and obtains values that are all very close together but consistently 0.05 mm larger than the true value. Which description applies?

  1. The readings are both accurate and precise.
  2. The readings are accurate but not precise.
  3. The readings are neither precise nor accurate.
  4. The readings are precise but not accurate. Correct answer.

Explanation

Precision refers to how closely repeated readings agree with each other, while accuracy refers to closeness to the true value. Consistent readings that are all offset by the same amount indicate a systematic error, giving high precision but poor accuracy.

Question 26Mechanics and Properties of Matter

A cyclist travels 150 m due east and then 200 m due north. What is the magnitude of the cyclist's resultant displacement?

  1. 50 m
  2. 175 m
  3. 350 m
  4. 250 m Correct answer.

Explanation

The two displacements are perpendicular, so the resultant is found from Pythagoras: the square root of (150 squared plus 200 squared) equals the square root of 62 500, which is 250 m. Displacement is the straight-line vector from start to finish, not the total path length.

Question 27Mechanics and Properties of Matter

Which statement correctly describes the acceleration of a body moving with uniform velocity?

  1. The acceleration acts perpendicular to the velocity.
  2. The acceleration is constant and non-zero in the direction of motion.
  3. The acceleration is zero because the velocity is constant. Correct answer.
  4. The acceleration increases steadily with time.

Explanation

Acceleration is the rate of change of velocity, so if the velocity vector does not change in magnitude or direction the acceleration is zero. A body with uniform velocity therefore has no net force acting on it, consistent with Newton's first law.

Question 28Mechanics and Properties of Matter

A ball is dropped from rest and falls freely for 3.0 s. Taking g = 9.8 m s⁻² and neglecting air resistance, how far does it fall?

  1. 88 m
  2. 9.8 m
  3. 29 m
  4. 44 m Correct answer.

Explanation

Using s = ut + ½at² with u = 0 gives s = ½ × 9.8 × 3.0² = 44.1 m, which rounds to 44 m. The distance depends on the square of the time, not linearly on it.

Question 29Mechanics and Properties of Matter

A newton is equivalent to which combination of base SI units?

  1. kg m⁻¹ s⁻²
  2. kg m s⁻² Correct answer.
  3. kg m s⁻¹
  4. kg m² s⁻²

Explanation

Force equals mass times acceleration, so the newton is one kilogram metre per second squared. This follows directly from F = ma with mass in kg and acceleration in m s⁻².

Question 30Mechanics and Properties of Matter

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

  1. The drag force is greater than the weight, so the skydiver decelerates.
  2. The weight equals the total drag force, so the resultant force is zero. Correct answer.
  3. The weight is greater than the drag force, so the skydiver keeps accelerating.
  4. There are no forces acting on the skydiver at terminal velocity.

Explanation

At terminal velocity the speed is constant, so the acceleration is zero and the resultant force must be zero. The downward weight is therefore exactly balanced by the upward drag force.

Question 31Mechanics and Properties of Matter

A force of 12 N acts on a body and moves it 5.0 m in the direction of the force. What is the work done by the force?

  1. 17 J
  2. 0 J
  3. 60 J Correct answer.
  4. 2.4 J

Explanation

Work done equals force times displacement in the direction of the force, so W = 12 × 5.0 = 60 J. The joule is the unit of work, equivalent to one newton metre.

Question 32Mechanics and Properties of Matter

Which of the following is the SI unit of the moment of a force about a point?

  1. J s
  2. N m Correct answer.
  3. N
  4. N m⁻¹

Explanation

The moment of a force is force multiplied by the perpendicular distance from the pivot, so its unit is the newton metre. Although dimensionally similar to the joule, the newton metre is used for moments to distinguish it from energy.

Question 33Mechanics and Properties of Matter

A solid metal block has a mass of 540 g and a volume of 200 cm³. What is its density?

  1. 27 g cm⁻³
  2. 1.08 g cm⁻³
  3. 2.7 g cm⁻³ Correct answer.
  4. 0.37 g cm⁻³

Explanation

Density is mass divided by volume, so 540 g ÷ 200 cm³ = 2.7 g cm⁻³. This value is typical of aluminium, confirming the order of magnitude is sensible.

Question 34Mechanics and Properties of Matter

A crate of weight 400 N rests on a horizontal floor. What is the normal reaction force exerted by the floor on the crate?

  1. Zero, because the crate is at rest
  2. 800 N upwards
  3. 400 N downwards
  4. 400 N upwards Correct answer.

Explanation

The crate is in vertical equilibrium, so the upward normal reaction must balance the downward weight of 400 N. The normal reaction is a contact force from the floor and always acts perpendicular to the surface.

Question 35Mechanics and Properties of Matter

A car accelerates uniformly from 8.0 m s⁻¹ to 20 m s⁻¹ in 6.0 s. What is its acceleration?

  1. 1.3 m s⁻²
  2. 2.0 m s⁻² Correct answer.
  3. 3.3 m s⁻²
  4. 12 m s⁻²

Explanation

Acceleration is the change in velocity divided by the time taken: (20 − 8.0) ÷ 6.0 = 2.0 m s⁻². Using the change in velocity, not the final velocity, is essential.

Question 36Mechanics and Properties of Matter

A 1500 kg car travelling at 20 m s⁻¹ brakes uniformly and stops in 5.0 s. What is the average braking force?

  1. 6000 N Correct answer.
  2. 7500 N
  3. 300 N
  4. 30 000 N

Explanation

The deceleration is 20 ÷ 5.0 = 4.0 m s⁻², and Newton's second law gives F = ma = 1500 × 4.0 = 6000 N. Equivalently, the force equals the rate of change of momentum.

Question 37Mechanics and Properties of Matter

Two forces act on a particle: 10 N to the east and 10 N to the north. What is the direction of the resultant force?

  1. Due north
  2. Due east
  3. North-east, at 45° to each force Correct answer.
  4. North-west, at 45° to each force

Explanation

Two equal perpendicular forces give a resultant along their bisector, so it points north-east at 45° to each. The magnitude would be 10√2 N, but the direction depends only on the equal magnitudes.

Question 38Mechanics and Properties of Matter

A uniform metre rule of weight 1.2 N is pivoted at its centre. A 0.30 N weight hangs 30 cm from the pivot on the left. Where must a 0.20 N weight be hung to balance the rule?

  1. 30 cm from the pivot on the right
  2. 60 cm from the pivot on the right
  3. 45 cm from the pivot on the right Correct answer.
  4. 20 cm from the pivot on the right

Explanation

For rotational equilibrium the clockwise and anticlockwise moments must be equal: 0.30 × 30 = 0.20 × d, giving d = 9.0 ÷ 0.20 = 45 cm. The weight of the rule acts at the pivot, so it produces no moment.

Question 39Mechanics and Properties of Matter

A block slides down a rough incline at constant speed. Which statement about the energy changes is correct?

  1. The total mechanical energy of the block is conserved.
  2. The block gains potential energy as it descends.
  3. The kinetic energy increases as the block descends.
  4. The loss of gravitational potential energy appears as heat in the block and slope. Correct answer.

Explanation

At constant speed the kinetic energy does not change, so the decrease in gravitational potential energy is dissipated as heat by friction. Mechanical energy is therefore not conserved when friction does negative work.

Question 40Mechanics and Properties of Matter

A wire of length 3.0 m and cross-sectional area 2.0 × 10⁻⁶ m² has a Young modulus of 2.0 × 10¹¹ Pa. What extension is produced by a load of 400 N?

  1. 1.5 mm
  2. 6.0 mm
  3. 3.0 mm Correct answer.
  4. 0.30 mm

Explanation

From E = FL/(Ae), the extension e = FL/(AE) = (400 × 3.0) ÷ (2.0 × 10⁻⁶ × 2.0 × 10¹¹) = 3.0 × 10⁻³ m, that is 3.0 mm. The strain is the extension divided by the original length.

Question 41Mechanics and Properties of Matter

A sealed container holds a gas at constant temperature. If the volume is halved, what happens to the pressure?

  1. It quadruples, because pressure depends on the square of the volume.
  2. It halves, because pressure is directly proportional to volume.
  3. It stays the same, because the temperature is constant.
  4. It doubles, because pressure is inversely proportional to volume. Correct answer.

Explanation

Boyle's law states that for a fixed mass of gas at constant temperature, pV is constant, so halving the volume doubles the pressure. The result follows from the increased frequency of molecular collisions with the walls in a smaller volume.

Question 42Mechanics and Properties of Matter

A body moves in a circle at constant speed. Which quantity remains constant during the motion?

  1. The momentum vector
  2. The velocity vector
  3. The magnitude of the centripetal acceleration Correct answer.
  4. The direction of the centripetal force

Explanation

The centripetal acceleration has magnitude v²/r, and since both v and r are constant its magnitude is constant. Its direction, like that of the velocity and momentum, changes continuously as the body moves round the circle.

Question 43Mechanics and Properties of Matter

A uniform plank of weight 300 N and length 4.0 m rests on two supports, one at each end. A 500 N load is placed 1.0 m from the left end. What is the reaction at the left support?

  1. 525 N Correct answer.
  2. 800 N
  3. 275 N
  4. 400 N

Explanation

Taking moments about the right support: R_L × 4.0 = 500 × 3.0 + 300 × 2.0, so R_L = (1500 + 600) ÷ 4.0 = 525 N. The plank's weight acts at its centre, 2.0 m from either end.

Question 44Mechanics and Properties of Matter

A block of mass 2.0 kg is pulled along a rough horizontal floor by a horizontal force of 15 N. The friction force is 7.0 N. What is the acceleration of the block?

  1. 11 m s⁻²
  2. 4.0 m s⁻² Correct answer.
  3. 7.5 m s⁻²
  4. 3.5 m s⁻²

Explanation

The resultant horizontal force is 15 − 7.0 = 8.0 N, and Newton's second law gives a = 8.0 ÷ 2.0 = 4.0 m s⁻². Friction must be subtracted because it opposes the applied force.

Question 45Mechanics and Properties of Matter

A 0.50 kg ball moving at 4.0 m s⁻¹ collides head-on with a stationary 1.5 kg ball and they stick together. What is their common velocity after the collision?

  1. 2.0 m s⁻¹ in the original direction
  2. 4.0 m s⁻¹ in the original direction
  3. 1.0 m s⁻¹ in the original direction Correct answer.
  4. 0.67 m s⁻¹ in the opposite direction

Explanation

Momentum is conserved in the collision: 0.50 × 4.0 = (0.50 + 1.5) × v, so v = 2.0 ÷ 2.0 = 1.0 m s⁻¹. The combined mass moves in the direction of the original momentum.

Question 46Mechanics and Properties of Matter

A liquid flows steadily through a horizontal pipe that narrows from a cross-sectional area of 8.0 cm² to 2.0 cm². If the speed in the wide section is 1.5 m s⁻¹, what is the speed in the narrow section?

  1. 1.5 m s⁻¹
  2. 3.0 m s⁻¹
  3. 0.38 m s⁻¹
  4. 6.0 m s⁻¹ Correct answer.

Explanation

For an incompressible liquid the equation of continuity gives A₁v₁ = A₂v₂, so v₂ = (8.0 × 1.5) ÷ 2.0 = 6.0 m s⁻¹. The speed rises by the same factor by which the area falls.

Question 47Mechanics and Properties of Matter

A body of weight 20 N is fully immersed in water and displaces 1500 cm³ of water. Taking the density of water as 1000 kg m⁻³ and g = 9.8 m s⁻², what is the upthrust on the body?

  1. 1.5 N
  2. 20 N
  3. 9.8 N
  4. 14.7 N Correct answer.

Explanation

The upthrust equals the weight of fluid displaced: mass of displaced water = 1000 × 1.5 × 10⁻³ = 1.5 kg, so upthrust = 1.5 × 9.8 = 14.7 N. Since this is less than the weight, the body would sink.

Question 48Mechanics and Properties of Matter

A student measures the time for 20 oscillations of a simple pendulum and divides by 20 to find the period. Why is this better than timing a single oscillation?

  1. It makes the pendulum swing with a smaller amplitude.
  2. Dividing a longer measured time by 20 reduces the percentage uncertainty in the period. Correct answer.
  3. It eliminates systematic error in the stopwatch reading.
  4. It removes the effect of air resistance on the pendulum.

Explanation

Reaction-time error is roughly fixed, so timing many oscillations spreads it over a larger total time and reduces the percentage uncertainty in the period. It does not remove systematic errors or change the pendulum's motion.

Question 49Mechanics and Properties of Matter

A uniform ladder of weight 250 N and length 5.0 m leans against a smooth vertical wall, with its foot 3.0 m from the wall on rough horizontal ground. What is the minimum coefficient of friction needed to keep the ladder from slipping?

  1. 0.375 Correct answer.
  2. 0.750
  3. 0.500
  4. 0.167

Explanation

By Pythagoras the height reached is 4.0 m. Taking moments about the foot: N_wall × 4.0 = 250 × 1.5, giving N_wall = 93.75 N. The friction force must equal this, and with N_ground = 250 N the coefficient is 93.75 ÷ 250 = 0.375.

Question 50Mechanics and Properties of Matter

A ball is thrown horizontally at 12 m s⁻¹ from a cliff 45 m high. Taking g = 9.8 m s⁻² and neglecting air resistance, how far from the base of the cliff does it land?

  1. 36 m Correct answer.
  2. 24 m
  3. 12 m
  4. 55 m

Explanation

The fall time follows from 45 = ½ × 9.8 × t², giving t ≈ 3.03 s, and the horizontal distance is 12 × 3.03 ≈ 36 m. Horizontal and vertical motions are independent, so the horizontal speed is unchanged during the fall.