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NCEA L1 Physics & ESS study materials
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NCEA L1 Physics & ESS practice questions

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Question 1Physics

A student walks 3.0 m east, then 4.0 m north. What is the magnitude of the student's total displacement from the starting point?

  1. 7.0 m
  2. 1.0 m
  3. 12.0 m
  4. 5.0 m Correct answer.

Explanation

Displacement is the straight-line distance from start to finish, so the two perpendicular legs form a right triangle. Using Pythagoras, the magnitude is the square root of (3.0² + 4.0²), which gives 5.0 m. The directions are at right angles, so the legs combine vectorially rather than by simple addition.

Question 2Physics

Which quantity is a scalar?

  1. Displacement
  2. Speed Correct answer.
  3. Acceleration
  4. Velocity

Explanation

A scalar has magnitude only, with no direction. Speed describes how fast something moves without stating a direction, so it is a scalar. Velocity, acceleration and displacement all require a direction to be fully described, making them vectors.

Question 3Physics

A car travels at a constant speed of 20 m s⁻¹ for 15 s. How far does it travel?

  1. 1.3 m
  2. 4500 m
  3. 300 m Correct answer.
  4. 35 m

Explanation

For constant speed, distance equals speed multiplied by time. Multiplying 20 m s⁻¹ by 15 s gives 300 m. The seconds units cancel, leaving metres, which confirms the calculation.

Question 4Physics

A cyclist speeds up from 4 m s⁻¹ to 12 m s⁻¹ in 4.0 s. What is the magnitude of the cyclist's acceleration?

  1. 2.0 m s⁻² Correct answer.
  2. 8.0 m s⁻²
  3. 4.0 m s⁻²
  4. 3.0 m s⁻²

Explanation

Acceleration is the change in velocity divided by the time taken. The change in velocity is 12 − 4 = 8 m s⁻¹ over 4.0 s, giving 2.0 m s⁻². Dividing the velocity change by time keeps the units consistent.

Question 5Physics

A book rests on a horizontal table. Which statement correctly describes the forces acting on the book?

  1. Only gravity acts on the book, so it stays still.
  2. Gravity acts down and friction acts up; they balance the weight.
  3. Gravity acts down and the normal force acts up; they are equal and opposite. Correct answer.
  4. The normal force is larger than gravity, which keeps the book up.

Explanation

The book is in equilibrium, so the vertical forces must balance. Gravity pulls it downward while the table pushes upward with a normal force of equal magnitude. Because the net force is zero, the book remains at rest.

Question 6Physics

A 2.0 kg mass hangs from a spring balance calibrated in newtons. Taking g = 10 N kg⁻¹, what reading does the balance show?

  1. 0.20 N
  2. 20 N Correct answer.
  3. 5.0 N
  4. 2.0 N

Explanation

Weight is the force of gravity on a mass, calculated as mass times gravitational field strength. Multiplying 2.0 kg by 10 N kg⁻¹ gives 20 N. The kilogram units cancel, leaving newtons as required.

Question 7Physics

Which statement best describes what happens to the particles of a solid as it is heated and melts?

  1. The particles gain kinetic energy and break free of fixed positions to move past each other. Correct answer.
  2. The particles themselves melt and turn into liquid droplets.
  3. The particles stop vibrating and become completely still.
  4. The particles lose energy and pack more tightly together.

Explanation

Heating transfers energy to the particles, increasing their kinetic energy. In a solid the particles vibrate about fixed positions; at melting point they gain enough energy to overcome the forces holding them in place and can slide past one another. This change in arrangement is what makes the substance a liquid.

Question 8Physics

Which of the following is an example of a longitudinal wave?

  1. Light travelling through a vacuum
  2. A water wave on the surface of a lake
  3. A wave on a vibrating guitar string
  4. A sound wave travelling through air Correct answer.

Explanation

In a longitudinal wave the particles oscillate parallel to the direction of energy transfer. Sound in air is a series of compressions and rarefactions along the direction the wave travels, so it is longitudinal. Light, water surface waves and string waves are transverse, with oscillation perpendicular to travel.

Question 9Physics

A car accelerates uniformly from rest to 20 m s⁻¹ in 5.0 s. What distance does it cover during this time?

  1. 100 m
  2. 50 m Correct answer.
  3. 4.0 m
  4. 200 m

Explanation

For uniform acceleration from rest, the average velocity is half the final velocity, here 10 m s⁻¹. Multiplying this average velocity by 5.0 s gives 50 m. Alternatively, using d = ½at² with a = 4.0 m s⁻² gives the same result.

Question 10Physics

A force of 12 N acts on a 3.0 kg trolley on a frictionless surface. What is the trolley's acceleration?

  1. 4.0 m s⁻² Correct answer.
  2. 0.25 m s⁻²
  3. 15 m s⁻²
  4. 36 m s⁻²

Explanation

Newton's second law states that force equals mass times acceleration, so acceleration equals force divided by mass. Dividing 12 N by 3.0 kg gives 4.0 m s⁻². The units work out because one newton is one kilogram metre per second squared.

Question 11Physics

A 1500 kg car travelling at 10 m s⁻¹ brakes and stops in 2.0 s. What is the magnitude of the average braking force?

  1. 150 N
  2. 7500 N Correct answer.
  3. 3000 N
  4. 15000 N

Explanation

The deceleration is the change in velocity divided by time: 10 m s⁻¹ ÷ 2.0 s = 5.0 m s⁻². Applying F = ma gives 1500 kg × 5.0 m s⁻² = 7500 N. The force opposes the motion, so it acts opposite to the car's velocity.

Question 12Physics

A ball is dropped from a cliff and falls freely for 3.0 s before hitting the ground. Taking g = 10 m s⁻² and ignoring air resistance, how far does it fall?

  1. 15 m
  2. 30 m
  3. 90 m
  4. 45 m Correct answer.

Explanation

For free fall from rest, distance is given by d = ½gt². Substituting gives ½ × 10 × 3.0² = 45 m. The distance depends on the square of the time, so it is not simply g multiplied by time.

Question 13Physics

A wave has a frequency of 5.0 Hz and a wavelength of 2.0 m. What is its speed?

  1. 0.40 m s⁻¹
  2. 2.5 m s⁻¹
  3. 10 m s⁻¹ Correct answer.
  4. 7.0 m s⁻¹

Explanation

The wave equation relates speed, frequency and wavelength: v = f × λ. Multiplying 5.0 Hz by 2.0 m gives 10 m s⁻¹. Frequency is the number of waves per second, so each second the wave advances 5.0 wavelengths.

Question 14Physics

A light ray strikes a plane mirror at 30° to the normal. What is the angle between the reflected ray and the mirror surface?

  1. 90°
  2. 30°
  3. 120°
  4. 60° Correct answer.

Explanation

The law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal. The reflected ray is therefore 30° from the normal. Angles from the normal and from the mirror surface are complementary, so the angle to the surface is 90° − 30° = 60°.

Question 15Physics

A student adds a 50 g piece of metal at 100 °C to 100 g of water at 20 °C in an insulated cup. Which statement best explains the final temperature reached?

  1. The final temperature is 100 °C because the metal keeps its heat.
  2. The final temperature is between 20 °C and 100 °C, closer to 20 °C because water has a larger heat capacity and mass. Correct answer.
  3. The final temperature equals 60 °C, the average of the two starting temperatures.
  4. The final temperature is 20 °C because water cannot gain heat.

Explanation

Energy flows from the hot metal to the cooler water until both reach the same temperature. The final temperature lies between the two starting values, weighted by each substance's mass and specific heat capacity. The water has a larger mass and a higher specific heat capacity, so it warms only slightly, leaving the final temperature nearer 20 °C.

Question 16Physics

A 6.0 V battery is connected across a 3.0 Ω resistor in a simple series circuit. What current flows?

  1. 18 A
  2. 9.0 A
  3. 0.50 A
  4. 2.0 A Correct answer.

Explanation

Ohm's law states that voltage equals current times resistance, so current equals voltage divided by resistance. Dividing 6.0 V by 3.0 Ω gives 2.0 A. The units are consistent because one volt per ohm is one ampere.

Question 17Physics

Two identical resistors of 4.0 Ω are connected in parallel. What is the total resistance of the combination?

  1. 1.0 Ω
  2. 8.0 Ω
  3. 4.0 Ω
  4. 2.0 Ω Correct answer.

Explanation

For two equal resistors in parallel, the total resistance is half the value of one resistor. Here 4.0 Ω ÷ 2 = 2.0 Ω. Adding more parallel paths always lowers the total resistance below the smallest individual resistor.

Question 18Physics

A current of 2.0 A flows through a 5.0 Ω resistor for 10 s. How much energy is transferred to the resistor?

  1. 1000 J
  2. 100 J
  3. 200 J Correct answer.
  4. 20 J

Explanation

Power dissipated in a resistor is I²R, giving (2.0)² × 5.0 = 20 W. Energy is power multiplied by time, so 20 W × 10 s = 200 J. This energy appears as heat in the resistor.

Question 19Physics

A wooden block floats in water with part of its volume above the surface. Which statement best explains why it floats?

  1. Water pushes down on the block harder than gravity pulls it down.
  2. The upthrust equals the block's weight, and the block is less dense than water. Correct answer.
  3. The block's density is greater than water's, so it stays on top.
  4. The block is weightless in water, so no forces act on it.

Explanation

A floating object is in equilibrium, so the upward buoyant force (upthrust) equals its weight. This balance occurs when the object's average density is less than that of the fluid, so it displaces a weight of fluid equal to its own weight. The block settles until just enough volume is submerged to provide that upthrust.

Question 20Physics

A student measures the extension of a spring for several hanging masses and plots a graph of force against extension. The graph is a straight line through the origin up to a point, then curves. What does the straight section show?

  1. The spring's stiffness decreases as the force increases on the straight section.
  2. The extension is proportional to the square of the force.
  3. The spring obeys Hooke's law, with force proportional to extension. Correct answer.
  4. The spring has reached its elastic limit along the entire line.

Explanation

Hooke's law states that the extension of a spring is directly proportional to the applied force, provided the elastic limit is not exceeded. A straight line through the origin on a force–extension graph is exactly this proportional relationship. The curve beyond the line indicates the spring has passed its elastic limit and no longer obeys the law.

Question 21Physics

A satellite orbits Earth in a circular path at constant speed. Which statement best describes the forces and motion?

  1. A net force acts toward Earth's centre, changing the satellite's direction but not its speed. Correct answer.
  2. The satellite's velocity is constant because the orbit is circular.
  3. A net force acts along the direction of motion, increasing the satellite's speed.
  4. No force acts on the satellite because its speed is constant.

Explanation

Even at constant speed, the satellite's direction changes continuously, so its velocity changes and it must be accelerating. The gravitational force points toward Earth's centre, providing the centripetal force needed for circular motion. This force is perpendicular to the velocity, so it changes direction but not speed.

Question 22Physics

A crate is pushed across a rough floor at constant velocity by a horizontal force of 40 N. Which statement is correct?

  1. The friction force is 40 N, so the net horizontal force is zero. Correct answer.
  2. The friction force is greater than 40 N, which is why the crate moves steadily.
  3. The friction force is zero because the crate is moving.
  4. The pushing force is greater than friction, giving a net force forward.

Explanation

Constant velocity means the acceleration is zero, so by Newton's second law the net horizontal force must be zero. The applied push of 40 N is therefore balanced by an equal friction force of 40 N acting backward. A net force would cause the crate to speed up or slow down.

Question 23Physics

An object is placed 30 cm from a converging lens of focal length 10 cm. Using the lens formula, where is the image formed?

  1. 15 cm on the opposite side of the lens from the object Correct answer.
  2. 7.5 cm on the opposite side of the lens from the object
  3. 20 cm on the same side as the object
  4. 30 cm on the opposite side of the lens from the object

Explanation

The lens formula is 1/f = 1/do + 1/di, where distances are measured from the lens. Substituting 1/10 = 1/30 + 1/di gives 1/di = 1/10 − 1/30 = 2/30, so di = 15 cm. A positive image distance means a real image on the opposite side of the lens from the object.

Question 24Physics

A 0.50 kg ball moving at 6.0 m s⁻¹ collides head-on with a stationary 0.50 kg ball on a frictionless surface. After the collision the first ball stops. What is the velocity of the second ball?

  1. 0 m s⁻¹
  2. 12 m s⁻¹ in the original direction
  3. 6.0 m s⁻¹ in the original direction Correct answer.
  4. 3.0 m s⁻¹ in the original direction

Explanation

On a frictionless surface, total momentum is conserved in the collision. Initial momentum is 0.50 kg × 6.0 m s⁻¹ = 3.0 kg m s⁻¹, and since the first ball stops, all of it transfers to the second. Dividing 3.0 kg m s⁻¹ by 0.50 kg gives 6.0 m s⁻¹ in the original direction.

Question 25Physics

A student compares two waves on a string: wave A has twice the frequency of wave B, but both travel on the same string. Which statement best explains how their speeds and wavelengths compare?

  1. Both waves travel at the same speed and have equal wavelengths.
  2. Wave A travels twice as fast and has the same wavelength as wave B.
  3. Both waves travel at the same speed, and wave A has half the wavelength of wave B. Correct answer.
  4. Wave A travels at half the speed and has twice the wavelength of wave B.

Explanation

Wave speed on a string depends on the tension and mass per unit length of the string, not on frequency, so both waves travel at the same speed. From v = f × λ, if frequency doubles while speed stays constant, wavelength must halve. Hence wave A has half the wavelength of wave B.

Question 26Physics

Which of the following gives the correct SI unit for each quantity: work, power, and pressure?

  1. Work in joules, power in watts, pressure in pascals Correct answer.
  2. Work in joules, power in pascals, pressure in watts
  3. Work in watts, power in joules, pressure in newtons
  4. Work in newtons, power in watts, pressure in joules

Explanation

Work is energy transferred and is measured in joules, defined as one newton-metre. Power is the rate of doing work, measured in watts, where one watt equals one joule per second. Pressure is force per unit area and is measured in pascals, equal to one newton per square metre.

Question 27Physics

A student measures the mass of a metal block five times and obtains 24.8 g, 25.1 g, 25.0 g, 24.9 g and 25.2 g. Which statement best describes these measurements?

  1. They are accurate but not precise
  2. They are both precise and accurate
  3. They are precise but may not be accurate Correct answer.
  4. They are neither precise nor accurate

Explanation

Precision describes how closely repeated measurements agree with each other, while accuracy describes how close they are to the true value. These readings cluster within about 0.4 g of each other, so they are precise. Without knowing the accepted value, we cannot confirm accuracy, so they may be inaccurate if all are offset from the true mass.

Question 28Physics

A student measures the length of a pendulum as 0.842 m using a metre ruler. Which statement about this measurement is correct?

  1. It has two significant figures
  2. It has three significant figures
  3. It has four significant figures Correct answer.
  4. It has five significant figures

Explanation

Significant figures count all the certain digits plus one estimated digit. In 0.842, the leading zero is not significant, but the digits 8, 4 and 2 all are, giving three significant figures.

Question 29Physics

A cyclist travels 120 m east, then turns and travels 80 m west. What is the magnitude of the cyclist's displacement?

  1. 120 m
  2. 80 m
  3. 200 m
  4. 40 m Correct answer.

Explanation

Displacement is a vector measured from the starting position to the finishing position. The eastward and westward journeys are in opposite directions, so they partially cancel: 120 m minus 80 m leaves 40 m east. Distance travelled would be 200 m, but that is not displacement.

Question 30Physics

A car's velocity changes from 8.0 m s⁻¹ to 20 m s⁻¹ in 4.0 s while moving in a straight line. What is the car's acceleration?

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

Explanation

Acceleration is the change in velocity divided by the time taken. The change in velocity is 20 minus 8.0, which equals 12 m s⁻¹. Dividing by 4.0 s gives 3.0 m s⁻².

Question 31Physics

A skydiver falls at a steady terminal velocity of 50 m s⁻¹. Which statement best explains why the skydiver's speed stays constant?

  1. Air resistance exceeds the weight, so the skydiver slows down
  2. Air resistance equals the weight, so the net force is zero Correct answer.
  3. The weight is larger than air resistance, so acceleration continues
  4. Gravity stops acting on the skydiver once terminal velocity is reached

Explanation

At terminal velocity the downward weight is balanced by the upward air resistance. With zero net force, by Newton's first law the skydiver continues at constant velocity. Gravity never switches off; it is simply balanced by drag.

Question 32Physics

A 4.0 kg object rests on a horizontal table. Taking g = 10 N kg⁻¹, what is the normal force exerted by the table on the object?

  1. 0 N
  2. 4.0 N upward
  3. 40 N upward Correct answer.
  4. 40 N downward

Explanation

The object is at rest, so the vertical forces balance. The weight is mg, equal to 4.0 kg times 10 N kg⁻¹, giving 40 N downward. The normal force must therefore be 40 N upward to give zero net force.

Question 33Physics

A force of 30 N is applied to a lever at a distance of 0.50 m from the pivot. What moment does this force produce about the pivot?

  1. 15 N m Correct answer.
  2. 30 N m
  3. 0.017 N m
  4. 60 N m

Explanation

The moment of a force is the force multiplied by the perpendicular distance from the pivot. Here 30 N times 0.50 m gives 15 N m. The unit is the newton-metre.

Question 34Physics

Two workers carry a uniform 2.0 m plank of negligible mass by its ends. A 60 kg mass is placed 0.50 m from the left end. Taking g = 10 N kg⁻¹, what upward force must the left worker apply?

  1. 450 N Correct answer.
  2. 300 N
  3. 150 N
  4. 600 N

Explanation

Take moments about the right end. The load weight 600 N acts 1.5 m from the right end, giving a clockwise moment of 900 N m. The left worker's force acts 2.0 m from the right end, so it must equal 900 divided by 2.0, which is 450 N.

Question 35Physics

A ball is kicked horizontally at 12 m s⁻¹ from the top of a cliff and lands at the base. Taking g = 10 m s⁻² and ignoring air resistance, how long is the ball in the air if the cliff is 45 m high?

  1. 1.5 s
  2. 4.5 s
  3. 9.0 s
  4. 3.0 s Correct answer.

Explanation

Vertical and horizontal motion are independent, and the vertical motion starts from rest. Using s = ½gt², we get 45 = 5t², so t² = 9 and t = 3.0 s. The horizontal speed does not affect the fall time.

Question 36Physics

A 1200 kg car travelling at 15 m s⁻¹ collides with a stationary 800 kg car and the two lock together. What is their common velocity immediately after the collision?

  1. 11 m s⁻¹
  2. 7.5 m s⁻¹
  3. 9.0 m s⁻¹ Correct answer.
  4. 15 m s⁻¹

Explanation

In a perfectly inelastic collision, total momentum is conserved. Initial momentum is 1200 times 15, giving 18 000 kg m s⁻¹. The combined mass is 2000 kg, so the common velocity is 18 000 divided by 2000, which is 9.0 m s⁻¹.

Question 37Physics

A 25 kg crate is lifted vertically through 3.0 m at constant speed. Taking g = 10 N kg⁻¹, how much gravitational potential energy does the crate gain?

  1. 750 J Correct answer.
  2. 2500 J
  3. 75 J
  4. 250 J

Explanation

Gain in gravitational potential energy equals mgh, where m is mass, g is gravitational field strength and h is the height gained. Here 25 kg times 10 N kg⁻¹ times 3.0 m gives 750 J. Lifting at constant speed means the work done equals the energy gain.

Question 38Physics

A machine raises a 200 N load through 2.0 m in 4.0 s. If the machine uses 500 J of energy from its power source, what is its efficiency?

  1. 40%
  2. 80% Correct answer.
  3. 100%
  4. 20%

Explanation

Useful output energy is 200 N times 2.0 m, which equals 400 J. Efficiency is useful output divided by total input, so 400 divided by 500 gives 0.80, or 80%. The remaining 100 J is wasted, mainly as heat.

Question 39Physics

Water at 4 °C is heated in a beaker. Which statement best describes what happens to the water particles during heating?

  1. They gain mass as heat is added
  2. They lose kinetic energy and vibrate less
  3. They gain kinetic energy and move faster on average Correct answer.
  4. They expand in size as each particle grows larger

Explanation

Heating transfers energy to the particles, increasing their average kinetic energy. This is seen as a rise in temperature. The particles themselves do not change size or mass; it is their motion that changes.

Question 40Physics

A 2.0 kg block of ice at 0 °C is melted completely. The specific latent heat of fusion of ice is 3.3 × 10⁵ J kg⁻¹. How much energy is required?

  1. 3.3 × 10⁵ J
  2. 6.6 × 10⁵ J Correct answer.
  3. 6.6 × 10⁶ J
  4. 1.65 × 10⁵ J

Explanation

Energy needed to melt a mass is the mass times the specific latent heat of fusion. Here 2.0 kg times 3.3 × 10⁵ J kg⁻¹ gives 6.6 × 10⁵ J. The temperature stays at 0 °C during melting.

Question 41Physics

A microwave oven transfers 60 000 J of energy to 0.50 kg of water. If the specific heat capacity of water is 4200 J kg⁻¹ °C⁻¹, what temperature rise occurs, assuming no losses?

  1. 29 °C Correct answer.
  2. 57 °C
  3. 7.1 °C
  4. 14 °C

Explanation

Using E = mcΔθ, the temperature rise is E divided by mc. Here 60 000 divided by (0.50 × 4200) gives 60 000 divided by 2100, which is about 29 °C.

Question 42Physics

A sound wave travels at 340 m s⁻¹ through air and has a wavelength of 0.50 m. What is its frequency?

  1. 680 Hz Correct answer.
  2. 170 Hz
  3. 340 Hz
  4. 0.0015 Hz

Explanation

The wave equation is speed equals frequency times wavelength. Rearranging gives frequency as speed divided by wavelength, so 340 divided by 0.50 equals 680 Hz.

Question 43Physics

A ray of light passes from air into glass and bends towards the normal. Which statement best explains this?

  1. Light slows down in glass, so it bends towards the normal Correct answer.
  2. Light changes colour as it enters glass
  3. Light speeds up in glass, so it bends towards the normal
  4. The glass reflects some light, causing the bend

Explanation

When light enters a denser medium such as glass, it slows down because the refractive index is higher. This change in speed at the boundary causes refraction towards the normal. Reflection may occur but does not cause the bending.

Question 44Physics

A student stands 2.0 m in front of a plane mirror. How far does the student's image appear to be from the student?

  1. 1.0 m
  2. 0 m
  3. 2.0 m
  4. 4.0 m Correct answer.

Explanation

A plane mirror forms a virtual image as far behind the mirror as the object is in front of it. The image is 2.0 m behind the mirror, so the total distance between student and image is 2.0 plus 2.0, which is 4.0 m.

Question 45Physics

A 12 V battery is connected to two resistors in series: 2.0 Ω and 4.0 Ω. What is the current in the circuit?

  1. 0.50 A
  2. 6.0 A
  3. 3.0 A
  4. 2.0 A Correct answer.

Explanation

In a series circuit the total resistance is the sum of the individual resistances, so 2.0 plus 4.0 equals 6.0 Ω. Using Ohm's law, current equals voltage divided by resistance, giving 12 divided by 6.0, which is 2.0 A.

Question 46Physics

A 60 W lamp is left on for 5.0 hours. How much energy does it transfer, in kilowatt-hours?

  1. 0.012 kWh
  2. 300 kWh
  3. 0.30 kWh Correct answer.
  4. 12 kWh

Explanation

Energy in kilowatt-hours equals power in kilowatts multiplied by time in hours. The lamp is 60 W, or 0.060 kW, and runs for 5.0 hours, giving 0.060 times 5.0, which is 0.30 kWh.

Question 47Physics

A student connects a 6.0 V battery across a resistor and measures a current of 0.30 A. The student then replaces the resistor with one of double the resistance. What current is measured?

  1. 0.30 A
  2. 0.60 A
  3. 0.15 A Correct answer.
  4. 1.2 A

Explanation

Ohm's law states that current is voltage divided by resistance, so for a fixed voltage, doubling the resistance halves the current. The original resistance is 6.0 divided by 0.30, which is 20 Ω. Doubling it to 40 Ω gives 6.0 divided by 40, which is 0.15 A.

Question 48Physics

An electromagnet is made by wrapping wire around an iron nail and connecting it to a battery. Which change would increase the strength of the electromagnet?

  1. Replacing the iron nail with a plastic rod
  2. Reversing the direction of the current
  3. Increasing the number of turns of wire around the nail Correct answer.
  4. Reducing the current through the wire

Explanation

The strength of an electromagnet depends on the current and the number of turns of wire. More turns produce a stronger magnetic field for the same current. The core material also matters, and iron is much better than plastic.

Question 49Physics

A 0.20 kg ball is whirled in a horizontal circle of radius 0.80 m at a constant speed of 4.0 m s⁻¹. What is the centripetal force required?

  1. 0.50 N
  2. 16 N
  3. 1.0 N
  4. 4.0 N Correct answer.

Explanation

Centripetal force equals mass times speed squared divided by radius. The speed squared is 16 m² s⁻², and multiplying by 0.20 kg gives 3.2, then dividing by 0.80 m gives 4.0 N. This force acts towards the centre of the circle.

Question 50Physics

A 2.0 kg mass hangs from a spring and extends it by 0.10 m. What is the spring constant of the spring? Take g = 10 N kg⁻¹.

  1. 200 N m⁻¹ Correct answer.
  2. 2.0 N m⁻¹
  3. 0.20 N m⁻¹
  4. 20 N m⁻¹

Explanation

Hooke's law states that force equals the spring constant times extension. The weight of the mass is 2.0 kg times 10 N kg⁻¹, which is 20 N. Rearranging gives the spring constant as 20 N divided by 0.10 m, which is 200 N m⁻¹.