I85PREP
⌘ K
DZI Physics and Astronomy study materials
DZI Physics and Astronomy study resources

DZI Physics and Astronomy practice questions

One question at a time. Build your DZI Physics and Astronomy 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 Gravitation

A car travels 150 m due east, then 120 m due west. What is the magnitude of its total displacement?

  1. 120 m
  2. 150 m
  3. 270 m
  4. 30 m Correct answer.

Explanation

Displacement is a vector, so opposite directions subtract. Taking east as positive gives 150 − 120 = 30 m, and the magnitude of that resultant is 30 m. Distance travelled would instead be 270 m.

Question 2Mechanics and Gravitation

An object moves in a straight line at constant velocity. Which statement about the net force on it is correct?

  1. The net force is zero Correct answer.
  2. The net force is constant but nonzero
  3. The net force increases with time
  4. The net force points opposite to the motion

Explanation

Newton's first law states that an object continues at constant velocity only when no net force acts on it. Constant velocity means zero acceleration, and Newton's second law then forces the net force to be zero.

Question 3Mechanics and Gravitation

Two masses, 2 kg and 8 kg, are separated by a distance r. If the separation is doubled to 2r, the gravitational force between them becomes

  1. twice the original
  2. one half of the original
  3. one quarter of the original Correct answer.
  4. four times the original

Explanation

Newton's law of gravitation gives F proportional to 1/r². Doubling r multiplies the force by 1/2² = 1/4, so the force falls to one quarter of its original value.

Question 4Mechanics and Gravitation

A satellite moves in a circular orbit around Earth. Which quantity remains constant throughout the orbit?

  1. Acceleration vector
  2. Net force vector
  3. Velocity
  4. Speed Correct answer.

Explanation

In a circular orbit the speed is fixed, while velocity, acceleration and net force all point in continuously changing directions. Those three are vectors whose directions rotate as the satellite goes around. Speed is the scalar magnitude and stays constant.

Question 5Mechanics and Gravitation

A book rests on a horizontal table. Which pair of forces forms a Newton's third law action-reaction pair?

  1. Earth pulls the book down; the book pulls Earth up
  2. The table pushes the book up; the book pushes the table down Correct answer.
  3. The book's weight; the normal force balancing it
  4. Earth pulls the book down; the table pushes the book up

Explanation

Third-law pairs act on two different bodies and are of the same type: the table pushes the book, and the book pushes the table. The weight and the normal force both act on the book, so they are not a third-law pair.

Question 6Mechanics and Gravitation

A block slides down a frictionless incline of angle 30°. Taking g = 10 m/s², what is its acceleration along the incline?

  1. 5 m/s² Correct answer.
  2. 10 m/s²
  3. 8.7 m/s²
  4. 0 m/s²

Explanation

The component of gravity along the incline is g sin θ. With θ = 30°, sin 30° = 0.5, so the acceleration is 10 × 0.5 = 5 m/s² down the slope.

Question 7Mechanics and Gravitation

A projectile is launched over level ground with no air resistance. At the highest point of its path, which statement is correct?

  1. Both velocity components are zero
  2. The vertical velocity is zero and the horizontal velocity is unchanged Correct answer.
  3. The horizontal velocity is zero and the vertical velocity is maximum
  4. The acceleration is zero

Explanation

The horizontal component of velocity stays constant because no horizontal force acts, while the vertical component decreases and passes through zero at the apex. The acceleration remains g downward throughout, including at the top.

Question 8Mechanics and Gravitation

A 1200 kg car accelerates uniformly from rest to 20 m/s in 8 s. What is the magnitude of the net force on the car?

  1. 9600 N
  2. 3000 N Correct answer.
  3. 150 N
  4. 2400 N

Explanation

The acceleration is Δv/Δt = 20/8 = 2.5 m/s². Newton's second law then gives F = ma = 1200 × 2.5 = 3000 N.

Question 9Mechanics and Gravitation

A planet orbits the Sun with semi-major axis 4 AU. Using Kepler's third law, what is its orbital period?

  1. 16 years
  2. 8 years Correct answer.
  3. 4 years
  4. 2 years

Explanation

For orbits about the Sun, P² = a³ when P is in years and a in AU. Here a³ = 64, so P = √64 = 8 years.

Question 10Mechanics and Gravitation

A 0.5 kg ball moving at 4 m/s strikes a wall and rebounds along the same line at 3 m/s. What is the magnitude of the impulse delivered to the ball?

  1. 3.5 kg·m/s Correct answer.
  2. 1.5 kg·m/s
  3. 2.0 kg·m/s
  4. 0.5 kg·m/s

Explanation

Impulse equals the change in momentum. Taking the incoming direction as positive, Δp = m(v_f − v_i) = 0.5(−3 − 4) = −3.5 kg·m/s, whose magnitude is 3.5 kg·m/s.

Question 11Mechanics and Gravitation

A uniform metre rule is pivoted at its centre. A 2 N weight hangs 30 cm to the left of the pivot. Where must a 3 N weight be placed to balance the rule?

  1. 30 cm to the right of the pivot
  2. 45 cm to the right of the pivot
  3. 15 cm to the right of the pivot
  4. 20 cm to the right of the pivot Correct answer.

Explanation

For rotational balance the moments about the pivot must be equal: 2 N × 30 cm = 3 N × d. Solving gives d = 60/3 = 20 cm on the opposite side.

Question 12Mechanics and Gravitation

A spring obeying Hooke's law is stretched by 4 cm and stores 0.8 J of elastic potential energy. What is the spring constant?

  1. 40 N/m
  2. 20 N/m
  3. 1000 N/m Correct answer.
  4. 400 N/m

Explanation

Elastic energy is U = ½kx². With x = 0.04 m, 0.8 = 0.5 × k × 0.0016, so k = 0.8/0.0008 = 1000 N/m.

Question 13Mechanics and Gravitation

A ball is thrown vertically upward. Ignoring air resistance, at what point in its flight is its acceleration greatest?

  1. At the highest point
  2. The acceleration is the same at every point of the flight Correct answer.
  3. Just before it returns to the hand
  4. Just after release

Explanation

Once released, the only force on the ball is gravity, so the acceleration is g downward at every instant. The speed changes, but the acceleration does not.

Question 14Mechanics and Gravitation

Two satellites orbit Earth at radii R and 4R from Earth's centre. What is the ratio of their orbital speeds, v(4R)/v(R)?

  1. 1/2 Correct answer.
  2. 4
  3. 2
  4. 1/4

Explanation

Circular orbital speed satisfies v² = GM/r, so v is proportional to 1/√r. Increasing the radius by a factor of 4 therefore reduces the speed by √4 = 2, giving a ratio of 1/2.

Question 15Mechanics and Gravitation

A skydiver falls at terminal velocity. Which statement correctly describes the forces at that moment?

  1. Air resistance equals the weight, so the net force is zero Correct answer.
  2. Both weight and air resistance are zero
  3. Air resistance exceeds the weight, so the skydiver decelerates
  4. The weight exceeds air resistance, so the skydiver accelerates

Explanation

Terminal velocity means the speed is constant, so the acceleration and hence the net force are zero. The upward drag must therefore exactly balance the downward weight.

Question 16Mechanics and Gravitation

A wheel of radius 0.4 m rotates at 5 rad/s. What is the linear speed of a point on its rim?

  1. 12.5 m/s
  2. 2.0 m/s Correct answer.
  3. 5.4 m/s
  4. 0.08 m/s

Explanation

For circular motion the tangential speed is v = ωr. Substituting gives v = 5 × 0.4 = 2.0 m/s.

Question 17Mechanics and Gravitation

A 3 kg object moves at 2 m/s and a 1 kg object moves at 6 m/s in the same direction. What is the speed of their centre of mass?

  1. 2 m/s
  2. 3 m/s Correct answer.
  3. 4 m/s
  4. 6 m/s

Explanation

The centre-of-mass velocity is the total momentum divided by the total mass. Total momentum is 3×2 + 1×6 = 12 kg·m/s and total mass is 4 kg, so v = 3 m/s.

Question 18Mechanics and Gravitation

A mass on a spring undergoes simple harmonic motion with amplitude A. At what displacement is the kinetic energy equal to the potential energy?

  1. x = A/√2 Correct answer.
  2. x = A/2
  3. x = A
  4. x = A/4

Explanation

Total energy is ½kA², and potential energy is ½kx². Setting ½kx² equal to half the total energy gives x² = A²/2, so x = A/√2, which is about 0.71A.

Question 19Mechanics and Gravitation

A satellite is in a circular orbit of radius r about a planet of mass M. Which expression gives its total mechanical energy, taking potential energy as zero at infinity?

  1. GMm/r
  2. −GMm/(2r) Correct answer.
  3. GMm/(2r)
  4. −GMm/r

Explanation

For a circular orbit, kinetic energy is +GMm/(2r) and potential energy is −GMm/r. Adding them gives a total of −GMm/(2r), which is negative and equal to half the potential energy.

Question 20Mechanics and Gravitation

A uniform solid sphere and a thin hoop of the same mass and radius roll without slipping down the same incline from rest. Which reaches the bottom first?

  1. The hoop, because its rotational inertia is smaller
  2. They arrive together because their masses and radii are equal
  3. The hoop, because more of its energy goes into rotation
  4. The solid sphere, because it has the smaller moment of inertia Correct answer.

Explanation

Rolling acceleration depends on the moment of inertia through a = g sinθ/(1 + I/(mr²)). The solid sphere has I = 2/5 mr² and the hoop has I = mr², so the sphere has the smaller denominator and the greater acceleration.

Question 21Mechanics and Gravitation

A particle moves under a conservative force. Which statement about its mechanical energy is necessarily true?

  1. The potential energy is constant along the motion
  2. The total mechanical energy is constant along the motion Correct answer.
  3. The kinetic energy is constant along the motion
  4. The total mechanical energy decreases steadily

Explanation

A conservative force has a potential energy function, and no non-conservative work is done. As a result kinetic and potential energy interchange while their sum stays fixed.

Question 22Mechanics and Gravitation

A planet of mass m orbits the Sun of mass M in an elliptical orbit with semi-major axis a. Which quantity is conserved along the orbit?

  1. Kinetic energy of the planet
  2. Speed of the planet
  3. Angular momentum about the Sun Correct answer.
  4. Distance from the Sun

Explanation

The gravitational force is central, so it exerts no torque about the Sun and angular momentum is conserved. This is why the planet sweeps equal areas in equal times. Distance, speed and kinetic energy all vary around an ellipse.

Question 23Mechanics and Gravitation

A force of 10 N acts on a 2 kg object for 3 s. What is the change in the object's velocity?

  1. 5 m/s
  2. 15 m/s Correct answer.
  3. 30 m/s
  4. 1.7 m/s

Explanation

Impulse equals change in momentum: FΔt = 10 × 3 = 30 N·s. Dividing by the mass gives Δv = 30/2 = 15 m/s.

Question 24Mechanics and Gravitation

An object is in static equilibrium. Which conditions must be satisfied?

  1. The net force must be zero but the net torque may be nonzero
  2. Only the net torque must be zero
  3. Only the net force must be zero
  4. Net force and net torque must both be zero Correct answer.

Explanation

Static equilibrium requires no translational acceleration and no rotational acceleration. That means both the vector sum of forces and the sum of torques about any point must vanish.

Question 25Mechanics and Gravitation

A stone is dropped from rest and falls freely for 3 s. Taking g = 10 m/s² and ignoring air resistance, how far has it fallen?

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

Explanation

Starting from rest, distance is s = ½gt². Substituting gives 0.5 × 10 × 9 = 45 m.

Question 26Mechanics and Gravitation

A block of mass 2 kg is pulled across a rough horizontal surface by a horizontal force of 10 N. The coefficient of kinetic friction between the block and the surface is 0.25. Taking g = 10 m/s², what is the acceleration of the block?

  1. 5.0 m/s²
  2. 7.5 m/s²
  3. 2.5 m/s² Correct answer.
  4. 10 m/s²

Explanation

The frictional force is f = μN = μmg = 0.25 × 2 × 10 = 5 N. The net horizontal force is 10 N − 5 N = 5 N, so the acceleration is a = F_net / m = 5 / 2 = 2.5 m/s².

Question 27Mechanics and Gravitation

A car travels around a circular track of radius 50 m at a constant speed of 20 m/s. What is the magnitude of its centripetal acceleration?

  1. 8 m/s² Correct answer.
  2. 0.4 m/s²
  3. 4 m/s²
  4. 20 m/s²

Explanation

Centripetal acceleration is given by a = v² / r. Substituting v = 20 m/s and r = 50 m gives a = (20²) / 50 = 400 / 50 = 8 m/s².

Question 28Mechanics and Gravitation

A satellite orbits a planet in a circular orbit. If the satellite's orbital radius is doubled while the planet's mass remains constant, by what factor does the orbital period change?

  1. It increases by a factor of 2.
  2. It increases by a factor of 4.
  3. It remains the same.
  4. It increases by a factor of 2√2. Correct answer.

Explanation

Kepler's third law states that T² ∝ r³ for circular orbits, so T ∝ r^(3/2). Doubling r multiplies T by 2^(3/2) = 2√2 ≈ 2.83.

Question 29Mechanics and Gravitation

A 5 kg object is lifted vertically at a constant speed of 2 m/s for 3 s. Taking g = 10 m/s², what is the work done by the lifting force?

  1. 30 J
  2. 100 J
  3. 300 J Correct answer.
  4. 600 J

Explanation

The lifting force equals the weight, F = mg = 5 × 10 = 50 N, because the object moves at constant speed. The displacement is s = vt = 2 × 3 = 6 m. Work done is W = Fs = 50 × 6 = 300 J.

Question 30Mechanics and Gravitation

A 2 kg object moving at 3 m/s collides head-on with a 4 kg object moving at 1 m/s in the opposite direction. They stick together. What is the velocity of the combined mass after the collision?

  1. 1.0 m/s in the direction of the 2 kg object
  2. 0.33 m/s in the direction of the 4 kg object
  3. 0.33 m/s in the direction of the 2 kg object Correct answer.
  4. 1.0 m/s in the direction of the 4 kg object

Explanation

Taking the direction of the 2 kg object as positive, initial momentum is (2)(3) + (4)(−1) = 6 − 4 = 2 kg·m/s. After sticking, total mass is 6 kg, so v = 2/6 = 0.33 m/s in the positive direction.

Question 31Mechanics and Gravitation

A simple pendulum has a period of 2 s on Earth. What is its approximate period on the Moon, where the acceleration due to gravity is about one-sixth that on Earth?

  1. 0.33 s
  2. 4.9 s Correct answer.
  3. 0.82 s
  4. 2 s

Explanation

The period of a simple pendulum is T = 2π√(L/g). If g is reduced by a factor of 6, T increases by a factor of √6 ≈ 2.45. Thus T ≈ 2 × 2.45 ≈ 4.9 s.

Question 32Mechanics and Gravitation

A 1500 kg car is traveling at 20 m/s when the driver applies the brakes, bringing the car to rest in a distance of 40 m. What is the magnitude of the average braking force?

  1. 30000 N
  2. 15000 N
  3. 3750 N
  4. 7500 N Correct answer.

Explanation

The work-energy theorem gives Fd = ½mv². Solving for F: F = (½ × 1500 × 20²) / 40 = (300000) / 40 = 7500 N.

Question 33Mechanics and Gravitation

A planet moves in an elliptical orbit around the Sun. At which point in its orbit is its orbital speed greatest?

  1. The speed is constant throughout the orbit
  2. At aphelion
  3. At the semi-minor axis endpoints
  4. At perihelion Correct answer.

Explanation

According to Kepler's second law, a planet sweeps out equal areas in equal times, so it moves fastest when it is closest to the Sun. The closest point is perihelion, where gravitational potential energy is lowest and kinetic energy is highest.

Question 34Mechanics and Gravitation

A uniform beam of length 4 m and weight 200 N is supported at its ends by two vertical pillars. A 300 N weight is placed on the beam 1 m from the left end. What is the magnitude of the supporting force at the left pillar?

  1. 200 N
  2. 300 N
  3. 250 N Correct answer.
  4. 150 N

Explanation

Taking moments about the right pillar: the beam's weight (200 N) acts at its center, 2 m from the right pillar, giving a moment of 200 × 2 = 400 N·m. The 200 N weight is 1 m from the left end, hence 3 m from the right pillar, giving a moment of 200 × 3 = 600 N·m. The left pillar force F_L acts at 4 m, so F_L × 4 = 400 + 600 = 1000 N·m, giving F_L = 250 N.

Question 35Mechanics and Gravitation

A 0.2 kg mass attached to a spring of spring constant 20 N/m is pulled 0.1 m from its equilibrium position and released from rest. What is the maximum speed of the mass during its oscillation?

  1. 0.5 m/s
  2. 1.0 m/s Correct answer.
  3. 4.0 m/s
  4. 2.0 m/s

Explanation

The maximum speed occurs at the equilibrium position, where all the elastic potential energy is converted to kinetic energy. Using ½kA² = ½mv², we get v = A√(k/m) = 0.1 × √(20/0.2) = 0.1 × √100 = 0.1 × 10 = 1.0 m/s.

Question 36Mechanics and Gravitation

A 1200 kg car is traveling at 20 m/s when the driver applies the brakes, bringing the car to rest in a distance of 40 m. What is the magnitude of the average braking force?

  1. 3750 N
  2. 15000 N
  3. 7500 N Correct answer.
  4. 30000 N

Explanation

The work-energy theorem gives Fd = ½mv². Solving for F: F = (½ × 1500 × 20²) / 40 = (300000) / 40 = 7500 N.

Question 37Thermodynamics and Statistical Physics

In an isothermal reversible expansion of an ideal gas, which quantity remains constant throughout the process?

  1. Volume
  2. Internal energy Correct answer.
  3. Entropy
  4. Pressure

Explanation

For an ideal gas the internal energy depends only on temperature, so at constant temperature the internal energy does not change and the heat absorbed equals the work done.

Question 38Thermodynamics and Statistical Physics

A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum thermodynamic efficiency?

  1. 0.50 Correct answer.
  2. 0.25
  3. 1.00
  4. 0.75

Explanation

The Carnot efficiency is one minus the ratio of cold to hot absolute temperature, giving 1 - 300/600 = 0.50. No engine working between these two reservoirs can exceed this value.

Question 39Thermodynamics and Statistical Physics

Which statement best expresses the second law of thermodynamics for an isolated system?

  1. The internal energy of an isolated system always rises
  2. The entropy of an isolated system never decreases Correct answer.
  3. The temperature of an isolated system is always uniform
  4. The pressure of an isolated system stays fixed

Explanation

The second law states that spontaneous processes in an isolated system increase total entropy, and in the reversible limit entropy stays constant, so it never decreases. This gives time its thermodynamic arrow.

Question 40Thermodynamics and Statistical Physics

An ideal gas is compressed adiabatically and reversibly. How does its temperature change?

  1. It stays the same
  2. It decreases
  3. It increases Correct answer.
  4. It changes only if the gas is diatomic

Explanation

With no heat exchange, work done on the gas raises its internal energy, and for an ideal gas that means a temperature rise. The adiabatic relation between temperature and volume confirms the heating on compression.

Question 41Thermodynamics and Statistical Physics

Which ensemble describes a system that can exchange energy with a large reservoir held at fixed temperature?

  1. Isolated ensemble
  2. Canonical ensemble Correct answer.
  3. Grand canonical ensemble
  4. Microcanonical ensemble

Explanation

The canonical ensemble fixes particle number, volume and temperature by coupling the system to a heat bath, so energy fluctuates. Its probability weights follow the Boltzmann factor.

Question 42Thermodynamics and Statistical Physics

A system absorbs 200 J of heat and does 50 J of work on its surroundings. What is the change in its internal energy?

  1. 150 J Correct answer.
  2. 50 J
  3. 250 J
  4. 200 J

Explanation

The first law gives the change in internal energy as heat added minus work done by the system, so 200 J - 50 J = 150 J. Sign conventions matter: heat in raises energy while work out lowers it.

Question 43Thermodynamics and Statistical Physics

For a monatomic ideal gas, what is the molar heat capacity at constant volume in units of the gas constant R?

  1. 1.5 R Correct answer.
  2. 2.5 R
  3. 3.0 R
  4. 3.5 R

Explanation

A monatomic gas has three translational degrees of freedom, each contributing R/2 to the molar heat capacity at constant volume, giving 3R/2. The constant-pressure value is larger by R.

Question 44Thermodynamics and Statistical Physics

In a reversible isothermal expansion of an ideal gas, what is the change in entropy of the gas when it expands from volume V to 2V at temperature T?

  1. nRT ln 2
  2. 0
  3. 2nR ln 2
  4. nR ln 2 Correct answer.

Explanation

Entropy change for an isothermal ideal-gas expansion is nR times the logarithm of the volume ratio, giving nR ln 2. The temperature cancels because the internal energy is unchanged.

Question 45Thermodynamics and Statistical Physics

A heat pump delivers 300 J of heat to a warm room while consuming 100 J of electrical work. What is its coefficient of performance for heating?

  1. 3 Correct answer.
  2. 1
  3. 2
  4. 4

Explanation

The heating coefficient of performance is heat delivered to the hot reservoir divided by work input, so 300/100 = 3. The remaining 200 J is drawn from the cold outdoor environment.

Question 46Thermodynamics and Statistical Physics

Which relation correctly defines the Helmholtz free energy and its natural variables?

  1. F = U + TS, with S and V natural
  2. F = U - TS, with T and V natural Correct answer.
  3. F = U - PV, with T and P natural
  4. F = H - TS, with T and V natural

Explanation

The Helmholtz free energy is internal energy minus temperature times entropy, and its natural variables are temperature and volume. It measures the useful work obtainable at constant temperature.

Question 47Thermodynamics and Statistical Physics

In the Maxwell-Boltzmann distribution for an ideal gas, how does the most probable molecular speed depend on temperature?

  1. It is proportional to the square of T
  2. It is proportional to T
  3. It is independent of T
  4. It is proportional to the square root of T Correct answer.

Explanation

The most probable speed equals the square root of 2kT/m, so it scales with the square root of absolute temperature. Raising temperature by a factor of four doubles this speed.

Question 48Thermodynamics and Statistical Physics

For a system at fixed temperature and pressure, which thermodynamic potential is minimized at equilibrium?

  1. Helmholtz free energy
  2. Internal energy
  3. Gibbs free energy Correct answer.
  4. Enthalpy

Explanation

At constant temperature and pressure the Gibbs free energy reaches a minimum at equilibrium, which is why it governs phase and reaction equilibria. The Helmholtz potential plays this role at constant temperature and volume instead.

Question 49Thermodynamics and Statistical Physics

A system has three equally probable microstates. What is its entropy in units of the Boltzmann constant k?

  1. 3
  2. 1/3
  3. 0
  4. ln 3 Correct answer.

Explanation

The Boltzmann formula gives entropy as k times the logarithm of the number of accessible microstates, so here it is k ln 3. Entropy is not the count itself but its logarithm.

Question 50Thermodynamics and Statistical Physics

In a canonical ensemble, the probability of finding a system in a state with energy E is proportional to which factor?

  1. exp(-kT/E)
  2. exp(E/kT)
  3. exp(-E/kT) Correct answer.
  4. exp(-E^2/kT)

Explanation

The Boltzmann factor weights each state by the exponential of minus its energy divided by kT, so lower-energy states are favored. The partition function normalizes these weights.