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Physics 30 Diploma study materials
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Physics 30 Diploma practice questions

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Question 1Physics 30

A proton is accelerated from rest through a potential difference of 500 V. What is the magnitude of the electric work done on the proton?

  1. 8.0 × 10⁻17 J Correct answer.
  2. 3.1 × 10⁻16 J
  3. 1.6 × 10⁻19 J
  4. 5.0 × 10⁻17 J

Explanation

The work done by the electric field equals the charge times the potential difference, W = qV. Using q = 1.60 × 10⁻19 C and V = 500 V gives W = 8.0 × 10⁻17 J. This energy appears as kinetic energy of the proton.

Question 2Physics 30

A wire carries a steady current of 3.0 A for 2.0 minutes. How much charge passes a point in the wire?

  1. 6.0 C
  2. 90 C
  3. 360 C Correct answer.
  4. 1.5 C

Explanation

Current is charge per unit time, so q = It. Converting 2.0 minutes to 120 s and multiplying by 3.0 A gives 360 C. Time must be in seconds when current is in amperes.

Question 3Physics 30

Which statement describes the direction of the magnetic force on a moving positive charge?

  1. It is parallel to the magnetic field direction.
  2. It is perpendicular to both the velocity and the magnetic field. Correct answer.
  3. It is opposite to the magnetic field direction.
  4. It is parallel to the velocity of the charge.

Explanation

The magnetic force is given by F = qv × B, a cross product. A cross product is perpendicular to both vectors that form it, so the force is perpendicular to both v and B. This is why the force does no work on the charge.

Question 4Physics 30

A photon has a frequency of 6.0 × 10¹⁴ Hz. What is its energy? (h = 6.63 × 10⁻34 J·s)

  1. 1.1 × 10⁻48 J
  2. 2.2 × 10⁻19 J
  3. 4.0 × 10⁻19 J Correct answer.
  4. 1.7 × 10⁻39 J

Explanation

Photon energy is E = hf. Multiplying 6.63 × 10⁻34 J·s by 6.0 × 10¹⁴ Hz gives about 4.0 × 10⁻19 J. This is a typical visible-light photon energy.

Question 5Physics 30

In a photoelectric experiment, increasing the intensity of incident light while keeping frequency constant causes which change?

  1. The maximum kinetic energy of emitted electrons increases.
  2. The number of photoelectrons emitted per second increases. Correct answer.
  3. The stopping voltage increases.
  4. The threshold frequency decreases.

Explanation

Intensity determines how many photons strike the surface per second, so more electrons are ejected per second. The energy of each photon depends only on frequency, so maximum kinetic energy and stopping voltage stay fixed.

Question 6Physics 30

A radioactive sample has a half-life of 8.0 days. What fraction of the original nuclei remains after 24 days?

  1. One half
  2. One sixteenth
  3. One quarter
  4. One eighth Correct answer.

Explanation

The elapsed time of 24 days equals three half-lives because 24 ÷ 8.0 = 3. Each half-life halves the remaining nuclei, so the fraction is (1/2)³ = 1/8.

Question 7Physics 30

Two point charges are separated by a distance r. If the distance is doubled while the charges stay the same, the electrostatic force becomes

  1. one half as large
  2. one quarter as large Correct answer.
  3. twice as large
  4. four times as large

Explanation

Coulomb's law states the force is inversely proportional to the square of the separation. Doubling r multiplies the denominator by four, so the force drops to one quarter of its original value.

Question 8Physics 30

Which quantity is conserved in every nuclear reaction?

  1. Number of neutrons
  2. Number of protons
  3. Total mass measured in kilograms
  4. Total charge Correct answer.

Explanation

Total electric charge is conserved in all nuclear reactions, including beta decay. Mass number is also conserved, but proton and neutron counts individually may change, and rest mass can convert to energy.

Question 9Physics 30

A proton moves with velocity 2.0 × 10⁶ m/s perpendicular to a uniform magnetic field of 0.50 T. What is the radius of its circular path? (m = 1.67 × 10⁻27 kg, q = 1.6 × 10⁻19 C)

  1. 0.042 m Correct answer.
  2. 0.084 m
  3. 0.010 m
  4. 0.021 m

Explanation

The magnetic force supplies centripetal force, so qvB = mv²/r and r = mv/(qB). Substituting gives r = (1.67 × 10⁻27 × 2.0 × 10⁶)/(1.6 × 10⁻19 × 0.50), which is about 0.042 m.

Question 10Physics 30

An electron is accelerated from rest through 250 V. What is its final speed? (m = 9.11 × 10⁻31 kg, e = 1.6 × 10⁻19 C)

  1. 6.6 × 10⁶ m/s
  2. 1.3 × 10⁷ m/s
  3. 4.4 × 10⁶ m/s
  4. 9.4 × 10⁶ m/s Correct answer.

Explanation

Set the electric work eV equal to kinetic energy ½mv². Solving v = √(2eV/m) with V = 250 V gives about 9.4 × 10⁶ m/s. This is well below the speed of light, so classical kinetic energy is valid.

Question 11Physics 30

A 12 V battery is connected to a 4.0 Ω resistor and a 2.0 Ω resistor in series. What is the current in the circuit?

  1. 3.0 A
  2. 6.0 A
  3. 2.0 A Correct answer.
  4. 1.0 A

Explanation

In series the resistances add, giving R = 6.0 Ω. Ohm's law then gives I = V/R = 12 V ÷ 6.0 Ω = 2.0 A. The same current flows through both resistors.

Question 12Physics 30

A wire of length 0.40 m carrying 5.0 A lies perpendicular to a 0.25 T magnetic field. What is the magnetic force on the wire?

  1. 0.50 N Correct answer.
  2. 1.0 N
  3. 0.05 N
  4. 0.10 N

Explanation

The force on a current-carrying wire is F = BIL sinθ. With θ = 90°, F = 0.25 T × 5.0 A × 0.40 m = 0.50 N. The direction follows from the right-hand rule.

Question 13Physics 30

A 200 g mass on a spring with constant 50 N/m oscillates. What is its period? (π ≈ 3.14)

  1. 0.20 s
  2. 1.3 s
  3. 0.40 s Correct answer.
  4. 2.5 s

Explanation

The period of a mass-spring system is T = 2π√(m/k). With m = 0.200 kg and k = 50 N/m, the square root is 0.0632 s, giving T ≈ 0.40 s. Mass must be in kilograms.

Question 14Physics 30

A light ray strikes a glass surface (n = 1.5) from air (n = 1.0) at an angle of incidence of 30°. What is the angle of refraction?

  1. 60°
  2. 30°
  3. 19° Correct answer.
  4. 48°

Explanation

Snell's law gives n₁sinθ₁ = n₂sinθ₂. So sinθ₂ = (1.0 × sin30°)/1.5 = 0.333, giving θ₂ ≈ 19°. Light bends toward the normal when entering a denser medium.

Question 15Physics 30

A concave mirror has a focal length of 10 cm. An object is placed 30 cm from the mirror. Where is the image formed?

  1. 15 cm in front of the mirror Correct answer.
  2. 10 cm in front of the mirror
  3. 7.5 cm in front of the mirror
  4. 30 cm behind the mirror

Explanation

The mirror equation is 1/f = 1/d₀ + 1/dᵢ. Substituting f = 10 cm and d₀ = 30 cm gives 1/dᵢ = 1/10 − 1/30 = 1/15, so dᵢ = 15 cm. A positive image distance means a real image in front of the mirror.

Question 16Physics 30

A 2.0 kg object moving at 3.0 m/s collides with a stationary 1.0 kg object and they stick together. What is their common velocity after the collision?

  1. 2.0 m/s Correct answer.
  2. 3.0 m/s
  3. 1.0 m/s
  4. 1.5 m/s

Explanation

Momentum is conserved in an inelastic collision. Initial momentum is 2.0 kg × 3.0 m/s = 6.0 kg·m/s, and dividing by the total mass of 3.0 kg gives 2.0 m/s. Kinetic energy is not conserved here.

Question 17Physics 30

A 0.50 kg ball is dropped from rest and falls 5.0 m. What is its speed just before impact, ignoring air resistance? (g = 9.8 m/s²)

  1. 49 m/s
  2. 4.9 m/s
  3. 7.0 m/s
  4. 9.9 m/s Correct answer.

Explanation

Using conservation of energy, mgh = ½mv², so v = √(2gh). With g = 9.8 m/s² and h = 5.0 m, v = √98 ≈ 9.9 m/s. Mass cancels and does not affect the result.

Question 18Physics 30

A 60 W light bulb operates on 120 V. What is the resistance of the bulb?

  1. 2.0 Ω
  2. 0.50 Ω
  3. 240 Ω Correct answer.
  4. 7200 Ω

Explanation

Power can be written P = V²/R, so R = V²/P. Substituting gives R = (120)²/60 = 14400/60 = 240 Ω. This is a typical resistance for an incandescent bulb.

Question 19Physics 30

A nucleus of uranium-238 emits an alpha particle. What is the resulting nucleus?

  1. Protactinium-234
  2. Uranium-234
  3. Radium-234
  4. Thorium-234 Correct answer.

Explanation

An alpha particle is a helium nucleus with 2 protons and 4 nucleons. Removing it lowers the atomic number by 2 and the mass number by 4, giving thorium-234. Element identity is set by proton number.

Question 20Physics 30

A radioactive isotope has a half-life of 5.0 years. A sample initially contains 8.0 × 10²⁰ atoms. How many atoms remain after 15 years?

  1. 5.3 × 10¹⁹
  2. 1.0 × 10²⁰ Correct answer.
  3. 2.0 × 10²⁰
  4. 4.0 × 10²⁰

Explanation

Fifteen years is three half-lives because 15 ÷ 5.0 = 3. The remaining fraction is (1/2)³ = 1/8, and one eighth of 8.0 × 10²⁰ is 1.0 × 10²⁰ atoms.

Question 21Physics 30

A convex lens has a focal length of 15 cm. An object is placed 10 cm from the lens. Which describes the image?

  1. Virtual, upright, and enlarged Correct answer.
  2. Real, inverted, and enlarged
  3. Real, inverted, and reduced
  4. Virtual, upright, and reduced

Explanation

The object lies inside the focal length, so a convex lens forms a virtual, upright, magnified image. This is the arrangement of a magnifying glass. A real image forms only when the object is beyond the focal point.

Question 22Physics 30

A 2.0 kg block slides down a frictionless incline of height 3.0 m. What is its speed at the bottom? (g = 9.8 m/s²)

  1. 5.4 m/s
  2. 3.0 m/s
  3. 9.8 m/s
  4. 7.7 m/s Correct answer.

Explanation

On a frictionless incline, gravitational potential energy converts fully to kinetic energy, so v = √(2gh). With h = 3.0 m, v = √58.8 ≈ 7.7 m/s. The incline angle does not matter without friction.

Question 23Physics 30

A standing wave forms on a string fixed at both ends. The fundamental frequency is 120 Hz. What is the frequency of the third harmonic?

  1. 360 Hz Correct answer.
  2. 480 Hz
  3. 240 Hz
  4. 180 Hz

Explanation

For a string fixed at both ends, harmonics are integer multiples of the fundamental, so fₙ = nf₁. The third harmonic is 3 × 120 Hz = 360 Hz. The second harmonic would be 240 Hz.

Question 24Physics 30

A 0.020 kg bullet moving at 400 m/s embeds in a 1.98 kg block initially at rest on a frictionless surface. What is the speed of the block and bullet just after impact?

  1. 8.0 m/s
  2. 0.40 m/s
  3. 4.0 m/s Correct answer.
  4. 2.0 m/s

Explanation

Momentum is conserved: (0.020)(400) = (2.00)v. The initial momentum is 8.0 kg·m/s and the combined mass is 2.00 kg, giving v = 4.0 m/s. Kinetic energy is largely lost as heat and deformation.

Question 25Physics 30

A photon of wavelength 4.0 × 10⁻⁷ m strikes a metal with work function 2.0 × 10⁻19 J. What is the maximum kinetic energy of the emitted electron? (hc = 1.99 × 10⁻25 J·m)

  1. 2.0 × 10⁻19 J
  2. 5.0 × 10⁻19 J
  3. 1.0 × 10⁻19 J
  4. 3.0 × 10⁻19 J Correct answer.

Explanation

Photon energy is E = hc/λ = (1.99 × 10⁻25)/(4.0 × 10⁻7) ≈ 5.0 × 10⁻19 J. The photoelectric equation gives K = E − W = 5.0 × 10⁻19 − 2.0 × 10⁻19 = 3.0 × 10⁻19 J.

Question 26Physics 30

Which statement best describes the direction of the magnetic force on a positively charged particle moving in a uniform magnetic field?

  1. It is opposite to the magnetic field direction.
  2. It is perpendicular to both the velocity and the magnetic field. Correct answer.
  3. It is parallel to the magnetic field direction.
  4. It is parallel to the velocity of the particle.

Explanation

The magnetic force on a moving charge is given by F = qv × B. The cross product shows that the force is perpendicular to both the velocity and the magnetic field, so it can change the direction of motion but not the speed.

Question 27Physics 30

A photon has a frequency of 6.0 × 10¹⁴ Hz. What is its energy? (h = 6.63 × 10⁻³⁴ J·s)

  1. 4.0 × 10⁻¹⁹ J Correct answer.
  2. 1.1 × 10⁻⁴⁸ J
  3. 2.5 × 10⁻¹⁹ J
  4. 1.7 × 10⁻²⁰ J

Explanation

The energy of a photon is given by E = hf. Substituting h = 6.63 × 10⁻³⁴ J·s and f = 6.0 × 10¹⁴ Hz gives E ≈ 3.98 × 10⁻¹⁹ J, which rounds to 4.0 × 10⁻¹⁹ J.

Question 28Physics 30

In a nuclear fission reaction, a heavy nucleus splits into two lighter nuclei and several neutrons. Which quantity is conserved in this reaction?

  1. Mass number and charge Correct answer.
  2. Neither mass number nor charge
  3. Charge only
  4. Mass number only

Explanation

Nuclear reactions conserve both mass number (total number of nucleons) and electric charge. In fission, the sum of mass numbers and the sum of atomic numbers of the products equal those of the original nucleus plus any incident particle.

Question 29Physics 30

A beam of light travels from air into a transparent medium. If the angle of incidence is 45° and the angle of refraction is 30°, what is the index of refraction of the medium? (n_air = 1.00)

  1. 1.41 Correct answer.
  2. 1.73
  3. 0.71
  4. 1.22

Explanation

Snell's law states n₁ sin θ₁ = n₂ sin θ₂. With n₁ = 1.00, θ₁ = 45°, and θ₂ = 30°, n₂ = sin 45° / sin 30° ≈ 0.707 / 0.500 = 1.41.

Question 30Physics 30

Which of the following best describes the electric field at a point in space?

  1. The potential energy per unit charge at that point
  2. The charge per unit area at that point
  3. The force per unit positive charge at that point Correct answer.
  4. The total force on a test charge at that point

Explanation

Electric field strength is defined as the force experienced by a small positive test charge divided by the magnitude of that charge, E = F/q. It is a vector quantity with units of newtons per coulomb.

Question 31Physics 30

An electron and a proton are both accelerated from rest through the same potential difference. Which particle has the longer de Broglie wavelength?

  1. The electron Correct answer.
  2. It depends on the magnitude of the potential difference
  3. Both have the same wavelength
  4. The proton

Explanation

The de Broglie wavelength is λ = h/p. After acceleration through the same potential difference, the electron (with much smaller mass) gains a higher speed and thus a smaller momentum than the proton for the same kinetic energy, giving it a longer wavelength.

Question 32Physics 30

A radioactive sample has a half-life of 12 hours. What fraction of the original activity remains after 36 hours?

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

Explanation

The number of half-lives is 36 h / 12 h = 3. After each half-life the activity halves, so after three half-lives the remaining fraction is (1/2)³ = 1/8.

Question 33Physics 30

Which of the following is an example of an inertial reference frame?

  1. A car moving at constant velocity on a straight highway Correct answer.
  2. A car rounding a curve at constant speed
  3. A car accelerating from rest
  4. A car braking to a stop

Explanation

An inertial frame is one in which Newton's first law holds: an object with no net force moves at constant velocity. A car moving at constant velocity (constant speed in a straight line) is an inertial frame.

Question 34Physics 30

A 2.0 kg object moving at 3.0 m/s collides elastically with a stationary 1.0 kg object. After the collision, the 2.0 kg object moves at 1.0 m/s in the same direction. What is the velocity of the 1.0 kg object?

  1. 4.0 m/s in the same direction Correct answer.
  2. 2.0 m/s in the same direction
  3. 3.0 m/s in the opposite direction
  4. 1.0 m/s in the opposite direction

Explanation

Momentum is conserved: (2.0)(3.0) + (1.0)(0) = (2.0)(1.0) + (1.0)v. Solving gives 6.0 = 2.0 + v, so v = 4.0 m/s in the original direction. In an elastic collision, kinetic energy is also conserved; checking: initial KE = 9.0 J, final KE = 0.5(2.0)(1.0)² + 0.5(1.0)(4.0)² = 1.0 + 8.0 = 9.0 J, confirming the result.

Question 35Physics 30

A 5.0 μF capacitor is charged to 12 V. What is the energy stored in the capacitor?

  1. 6.0 × 10⁻⁵ J
  2. 7.2 × 10⁻⁴ J
  3. 1.4 × 10⁻³ J
  4. 3.6 × 10⁻⁴ J Correct answer.

Explanation

The energy stored in a capacitor is U = ½CV². Substituting C = 5.0 × 10⁻⁶ F and V = 12 V gives U = 0.5 × 5.0 × 10⁻⁶ × 144 = 3.6 × 10⁻⁴ J.

Question 36Physics 30

A 0.50 kg mass attached to a spring oscillates with a period of 2.0 s. What is the spring constant? (π ≈ 3.14)

  1. 2.5 N/m
  2. 0.79 N/m
  3. 9.8 N/m
  4. 4.9 N/m Correct answer.

Explanation

The period of a mass-spring system is T = 2π√(m/k). Rearranging gives k = 4π²m/T². Substituting m = 0.50 kg and T = 2.0 s gives k = 4 × 9.87 × 0.50 / 4.0 ≈ 4.9 N/m.

Question 37Physics 30

A convex lens has a focal length of 20 cm. An object is placed 30 cm from the lens. What is the image distance?

  1. 60 cm on the opposite side of the lens Correct answer.
  2. 12 cm on the same side as the object
  3. 60 cm on the same side as the object
  4. 12 cm on the opposite side of the lens

Explanation

The thin-lens equation is 1/f = 1/do + 1/di. With f = +20 cm and do = 30 cm, 1/di = 1/20 - 1/30 = 1/60, so di = +60 cm. A positive image distance for a convex lens means a real image on the opposite side of the lens.

Question 38Physics 30

A 10 Ω resistor and a 20 Ω resistor are connected in parallel across a 12 V battery. What is the total current drawn from the battery?

  1. 0.80 A
  2. 0.40 A
  3. 1.8 A Correct answer.
  4. 1.2 A

Explanation

The equivalent resistance of parallel resistors is 1/R = 1/10 + 1/20 = 3/20, so R = 20/3 ≈ 6.67 Ω. The total current is I = V/R = 12 / 6.67 ≈ 1.8 A.

Question 39Physics 30

A proton moves at 2.0 × 10⁵ m/s perpendicular to a 0.30 T magnetic field. What is the radius of its circular path? (m = 1.67 × 10⁻²⁷ kg, q = 1.6 × 10⁻¹⁹ C)

  1. 7.0 × 10⁻³ m Correct answer.
  2. 1.4 × 10⁻² m
  3. 3.5 × 10⁻³ m
  4. 2.1 × 10⁻³ m

Explanation

The magnetic force provides the centripetal force: qvB = mv²/r, so r = mv/(qB). Substituting the values gives r = (1.67 × 10⁻²⁷)(2.0 × 10⁵) / ((1.6 × 10⁻¹⁹)(0.30)) ≈ 7.0 × 10⁻³ m.

Question 40Physics 30

In a photoelectric experiment, light of wavelength 400 nm is incident on a metal with work function 2.0 eV. What is the maximum kinetic energy of the emitted electrons? (hc = 1240 eV·nm)

  1. 0.50 eV
  2. 1.1 eV Correct answer.
  3. 5.1 eV
  4. 3.1 eV

Explanation

The photon energy is E = hc/λ = 1240 eV·nm / 400 nm = 3.1 eV. The maximum kinetic energy is Kmax = E - φ = 3.1 eV - 2.0 eV = 1.1 eV.

Question 41Physics 30

A nucleus of radon-222 undergoes alpha decay. Which nucleus is produced?

  1. Radon-221
  2. Radium-226
  3. Polonium-218 Correct answer.
  4. Lead-214

Explanation

Alpha decay emits an alpha particle (⁴₂He), so the mass number decreases by 4 and the atomic number decreases by 2. Radon-222 (Z=86) becomes an isotope with Z=84 and A=218, which is polonium-218.

Question 42Physics 30

Two parallel wires carry currents in the same direction. Which statement describes the magnetic force between them?

  1. They exert no force on each other.
  2. They repel each other.
  3. They attract each other. Correct answer.
  4. The force depends on the direction of the currents relative to Earth's field.

Explanation

Each wire produces a magnetic field that exerts a force on the other wire. Using the right-hand rule, the field from one wire at the location of the other, combined with the current direction, gives an attractive force when the currents are parallel.

Question 43Physics 30

A 0.20 kg object attached to a spring with constant 80 N/m is pulled 0.10 m from equilibrium and released. What is its maximum speed?

  1. 4.0 m/s
  2. 0.20 m/s
  3. 2.0 m/s Correct answer.
  4. 0.40 m/s

Explanation

For simple harmonic motion, the maximum speed is v_max = A√(k/m). Substituting A = 0.10 m, k = 80 N/m, and m = 0.20 kg gives v_max = 0.10 × √400 = 0.10 × 20 = 2.0 m/s.

Question 44Physics 30

A 0.50 kg mass is attached to a string and swung in a horizontal circle of radius 0.80 m at a constant speed of 3.0 m/s. What is the tension in the string?

  1. 5.6 N Correct answer.
  2. 4.5 N
  3. 1.9 N
  4. 9.0 N

Explanation

The tension provides the centripetal force: T = mv²/r. Substituting m = 0.50 kg, v = 3.0 m/s, and r = 0.80 m gives T = 0.50 × 9.0 / 0.80 = 5.625 N ≈ 5.6 N.

Question 45Physics 30

A 2.0 kg block is pushed up a frictionless incline of angle 30° with an initial speed of 4.0 m/s. How far along the incline does it travel before stopping? (g = 9.8 m/s²)

  1. 1.6 m Correct answer.
  2. 3.3 m
  3. 0.82 m
  4. 2.0 m

Explanation

The acceleration along the incline is a = g sin θ = 9.8 × 0.50 = 4.9 m/s² downward along the slope. Using v² = v₀² + 2ad with v = 0 gives 0 = 16 - 2(4.9)d, so d = 16 / 9.8 ≈ 1.6 m.

Question 46Physics 30

A 0.10 kg ice cube at 0°C is placed in 0.50 kg of water at 20°C. Assuming no heat loss to the surroundings, what is the final temperature of the mixture? (L_f = 3.34 × 10⁵ J/kg, c_water = 4186 J/(kg·°C))

  1. 16°C
  2. 10°C
  3. 0°C
  4. 4.0°C Correct answer.

Explanation

Heat to melt the ice: Q_melt = m_ice L_f = 0.10 × 3.34 × 10⁵ = 3.34 × 10⁴ J. Heat lost by water cooling to 0°C: Q_water = 0.50 × 4186 × 20 = 4.186 × 10⁴ J. Since Q_water > Q_melt, all ice melts and the remaining heat warms the melted ice and cools the water. Let T be final temperature. Heat lost by original water = 0.50 × 4186 × (20 - T). Heat gained by melted ice = 0.10 × 4186 × T + 3.34 × 10⁴. Equating and solving gives T ≈ 4.0°C.

Question 47Physics 30

A 100-turn coil of area 0.020 m² rotates in a uniform magnetic field of 0.50 T. If the coil rotates at 60 revolutions per minute, what is the maximum induced emf? (π ≈ 3.14)

  1. 0.63 V
  2. 6.3 V Correct answer.
  3. 3.1 V
  4. 1.0 V

Explanation

The maximum emf induced in a rotating coil is ε_max = NABω, where ω is the angular frequency. Convert 60 rpm to rad/s: ω = 60 × 2π / 60 = 2π ≈ 6.28 rad/s. Then ε_max = 100 × 0.020 × 0.50 × 6.28 ≈ 6.28 V, which rounds to 6.3 V.

Question 48Physics 30

A 2.0 kg block on a frictionless horizontal surface is attached to a spring (k = 200 N/m) and undergoes simple harmonic motion with amplitude 0.10 m. At what displacement is the kinetic energy equal to the potential energy?

  1. 0.050 m
  2. 0.025 m
  3. 0.071 m Correct answer.
  4. 0.10 m

Explanation

Total energy E = ½kA². When kinetic energy equals potential energy, each is half the total: ½kx² = ½(½kA²), so x² = A²/2 and x = A/√2 = 0.10/1.414 ≈ 0.071 m.

Question 49Physics 30

A charged particle with charge q and mass m is accelerated from rest through a potential difference V and then enters a uniform magnetic field B perpendicular to its velocity. What is the radius of its circular path?

  1. (1/B)√(2qV/m)
  2. (1/B)√(2mV/q) Correct answer.
  3. (1/B)√(qV/m)
  4. (1/B)√(mV/q)

Explanation

The kinetic energy gained is qV = ½mv², so v = √(2qV/m). The magnetic force provides centripetal force: qvB = mv²/r, giving r = mv/(qB). Substituting v gives r = (m/(qB))√(2qV/m) = (1/B)√(2mV/q).

Question 50Physics 30

A 5.0 kg object moving at 4.0 m/s to the right collides with a 3.0 kg object moving at 2.0 m/s to the left. After the collision, the 5.0 kg object moves at 1.0 m/s to the right. What is the velocity of the 3.0 kg object?

  1. 1.0 m/s to the right
  2. 5.0 m/s to the left
  3. 3.0 m/s to the right Correct answer.
  4. 3.0 m/s to the left

Explanation

Take right as positive. Initial momentum = (5.0)(4.0) + (3.0)(-2.0) = 20 - 6 = 14 kg·m/s. Final momentum = (5.0)(1.0) + (3.0)v = 5 + 3v. Setting equal: 14 = 5 + 3v, so 3v = 9 and v = +3.0 m/s (to the right).