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BUET Undergraduate Admission Main Written Examination study materials
BUET Undergraduate Admission Main Written Examination study resources

BUET Undergraduate Admission Main Written Examination practice questions

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Question 1Physics

A body moves along a straight line with constant acceleration. Its velocity increases from 4 m/s to 12 m/s in 4 s. What distance does it cover in this interval?

  1. 64 m
  2. 16 m
  3. 32 m Correct answer.
  4. 48 m

Explanation

With uniform acceleration the average velocity equals the mean of the initial and final velocities, here (4 + 12)/2 = 8 m/s. Multiplying by the 4 s interval gives a distance of 32 m, which also follows from s = ut + ½at² with a = 2 m/s².

Question 2Physics

A projectile is launched at an angle to the horizontal on level ground, with air resistance neglected. At the highest point of its path, which statement about its acceleration is correct?

  1. It has a horizontal component equal to g.
  2. It equals g directed vertically downward. Correct answer.
  3. It equals g directed along the tangent to the path.
  4. It is zero because the vertical velocity vanishes there.

Explanation

Only gravity acts on the projectile after launch, so the acceleration is constant and equal to g pointing vertically downward at every instant, including the apex. The velocity becomes purely horizontal at the top, but velocity and acceleration are independent quantities.

Question 3Physics

A block slides down a rough inclined plane at constant speed. Which statement correctly describes the forces on the block?

  1. The net force on the block is zero. Correct answer.
  2. The net force is directed down the incline.
  3. The normal reaction equals the weight of the block.
  4. Friction exceeds the component of weight along the incline.

Explanation

Constant velocity means zero acceleration, so by Newton's second law the vector sum of all forces must be zero. The component of weight down the slope is exactly balanced by kinetic friction, and the normal reaction balances only the perpendicular component of weight.

Question 4Physics

Two bodies of masses m and 3m, initially at rest, are pushed apart by a compressed spring between them on a frictionless surface. What is the ratio of the speed of the lighter body to that of the heavier body?

  1. 9 : 1
  2. 1 : 1
  3. 1 : 3
  4. 3 : 1 Correct answer.

Explanation

The spring forces are internal, so total momentum stays zero: m·v₁ = 3m·v₂ in magnitude. Hence the lighter body moves three times faster, giving the ratio 3 : 1. Kinetic energies are not equal; the lighter body carries three times the kinetic energy.

Question 5Physics

A flywheel of moment of inertia 2 kg·m² rotates at 10 rad/s. What is its rotational kinetic energy?

  1. 20 J
  2. 100 J Correct answer.
  3. 200 J
  4. 10 J

Explanation

Rotational kinetic energy is ½Iω², so substituting I = 2 kg·m² and ω = 10 rad/s gives ½ × 2 × 100 = 100 J. Note that ω must be squared, which is the step most often missed.

Question 6Physics

The escape velocity from the surface of a planet of mass M and radius R, ignoring atmospheric resistance, is given by which expression?

  1. √(GM/2R)
  2. √(GM/R)
  3. √(2GM/R) Correct answer.
  4. 2GM/R

Explanation

Setting the total mechanical energy to zero at escape gives ½mv² = GMm/R, which yields v = √(2GM/R). The factor 2 arises because the kinetic energy is one half mv² while the potential energy magnitude is GMm/R.

Question 7Physics

A simple pendulum has a period T on Earth. On a planet where the acceleration due to gravity is one quarter of that on Earth, its period becomes

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

Explanation

The period of a simple pendulum is T = 2π√(L/g), so it varies inversely with the square root of g. Reducing g to one quarter multiplies the period by √4 = 2, giving 2T.

Question 8Physics

An ideal gas undergoes an isothermal expansion. Which quantity remains constant during the process?

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

Explanation

For an ideal gas the internal energy depends only on temperature, so it stays constant in an isothermal process. Pressure and volume both change inversely according to Boyle's law, and entropy increases as the gas expands.

Question 9Physics

Two identical waves travelling in opposite directions on a stretched string superpose. At a displacement node of the resulting standing wave, which quantity is maximum?

  1. Particle speed Correct answer.
  2. Wave amplitude
  3. Transverse displacement
  4. Particle acceleration

Explanation

At a node the displacement is always zero, so its rate of change, the particle speed, reaches its largest value as the wave passes through equilibrium. The amplitude at a node is zero, and the acceleration, proportional to displacement, is also zero.

Question 10Physics

Light of wavelength 600 nm in vacuum enters a medium of refractive index 1.5. What are its wavelength and frequency inside the medium?

  1. 400 nm and 3.3 × 10¹⁴ Hz
  2. 400 nm and 5.0 × 10¹⁴ Hz Correct answer.
  3. 600 nm and 5.0 × 10¹⁴ Hz
  4. 900 nm and 5.0 × 10¹⁴ Hz

Explanation

The frequency is fixed by the source: f = c/λ = (3 × 10⁸)/(600 × 10⁻⁹) = 5.0 × 10¹⁴ Hz. Inside the medium the speed falls to c/n, so the wavelength becomes 600/1.5 = 400 nm while the frequency is unchanged.

Question 11Physics

A convex lens of focal length 20 cm forms an image of an object placed 30 cm in front of it. Which description of the image is correct?

  1. Virtual, erect and magnified
  2. Real, inverted and magnified Correct answer.
  3. Virtual, erect and diminished
  4. Real, inverted and diminished

Explanation

Using 1/f = 1/v − 1/u with u = −30 cm and f = +20 cm gives v = +60 cm, a real image on the far side. The magnification m = v/u = −2 shows the image is inverted and twice as large as the object.

Question 12Physics

In Young's double-slit experiment, the separation between adjacent bright fringes on the screen is found to be 2 mm. If the whole apparatus is immersed in water of refractive index 4/3, the new fringe separation is approximately

  1. 0.5 mm
  2. 2.7 mm
  3. 1.5 mm Correct answer.
  4. 2.0 mm

Explanation

Fringe spacing is β = λD/d, so it scales with the wavelength in the surrounding medium. Water reduces the wavelength by a factor of 4/3, giving β = 2 × 3/4 = 1.5 mm.

Question 13Physics

A charged particle enters a uniform magnetic field with its velocity perpendicular to the field. Which statement about its subsequent motion is correct?

  1. It moves in a straight line with constant speed.
  2. It moves in a parabola with increasing speed.
  3. It moves in a circle at constant speed. Correct answer.
  4. It moves in a helix with increasing speed.

Explanation

The magnetic force qv × B is always perpendicular to the velocity, so it changes direction but not magnitude, acting as a centripetal force. The particle therefore travels in a circular path at constant speed, with radius mv/(qB).

Question 14Physics

Three identical resistors are connected in parallel across a battery of negligible internal resistance. If each resistor has resistance R, what is the equivalent resistance of the combination?

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

Explanation

For n identical resistors in parallel the equivalent resistance is R/n, because 1/R_eq = 1/R + 1/R + 1/R = 3/R. Hence the combination has resistance R/3, which is smaller than any single branch.

Question 15Physics

An alternating current is given by i = 10 sin(100πt) amperes. What is the rms value of this current?

  1. 10 A
  2. 14.1 A
  3. 7.07 A Correct answer.
  4. 5 A

Explanation

For a sinusoidal current the rms value is the peak divided by √2, so 10/√2 ≈ 7.07 A. The rms value is the steady direct current that would dissipate the same average power in a resistor.

Question 16Physics

In the photoelectric effect, increasing the intensity of incident light while keeping its frequency unchanged causes

  1. a decrease in the threshold frequency of the metal.
  2. an increase in the stopping potential.
  3. an increase in the number of photoelectrons emitted per second. Correct answer.
  4. an increase in the maximum kinetic energy of the emitted electrons.

Explanation

Intensity fixes the number of photons arriving per second, so a brighter beam liberates more electrons per second. The maximum kinetic energy depends only on the photon frequency and the work function, so it is unaffected by intensity.

Question 17Physics

The half-life of a radioactive nuclide is 20 days. What fraction of an initial sample remains undecayed after 60 days?

  1. 1/3
  2. 1/8 Correct answer.
  3. 1/6
  4. 1/64

Explanation

Sixty days corresponds to three half-lives, since 60/20 = 3. Each half-life halves the remaining amount, so the fraction left is (1/2)³ = 1/8.

Question 18Physics

A body of mass 2 kg moving at 6 m/s collides head-on with a stationary body of mass 4 kg and sticks to it. What is the speed of the combined body just after the collision?

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

Explanation

Momentum is conserved in a perfectly inelastic collision: 2 × 6 = (2 + 4) × v. Solving gives v = 12/6 = 2 m/s. Kinetic energy is not conserved, roughly two thirds being lost as heat and deformation.

Question 19Physics

A body of mass m hangs from a spring of force constant k and executes vertical oscillations. What is the angular frequency of the motion?

  1. k/m
  2. √(m/k)
  3. 2π√(k/m)
  4. √(k/m) Correct answer.

Explanation

The restoring force is proportional to displacement with constant k, so the angular frequency is ω = √(k/m). The static extension due to gravity shifts the equilibrium position but does not change the frequency.

Question 20Physics

A particle of charge q moves with velocity v parallel to a uniform magnetic field B. What is the magnitude of the magnetic force on the particle?

  1. qvB/2
  2. zero Correct answer.
  3. qB/v
  4. qvB

Explanation

The magnetic force is F = qvB sin θ, where θ is the angle between velocity and field. When the velocity is parallel to the field, θ = 0 and sin θ = 0, so no magnetic force acts on the particle.

Question 21Physics

A uniform metre rule of weight 2 N is pivoted at its centre. A 3 N weight hangs 20 cm to the left of the pivot. Where must a 2 N weight be hung to balance the rule?

  1. 30 cm to the right of the pivot Correct answer.
  2. 20 cm to the right of the pivot
  3. 15 cm to the right of the pivot
  4. 40 cm to the right of the pivot

Explanation

The weight of the rule acts at the pivot and creates no moment about it. For balance, 3 N × 20 cm = 2 N × d, giving d = 30 cm on the opposite side.

Question 22Physics

Water flows steadily through a horizontal pipe that narrows from a cross-sectional area A to A/3. If the speed in the wider section is v, what is the pressure drop between the two sections?

  1. 2ρv²
  2. ρv²
  3. 8ρv²
  4. 4ρv² Correct answer.

Explanation

Continuity gives the narrow-section speed as 3v because the area falls to one third. Bernoulli's equation for a horizontal pipe then gives ΔP = ½ρ[(3v)² − v²] = ½ρ(8v²) = 4ρv².

Question 23Physics

A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the maximum efficiency of this engine?

  1. 20%
  2. 40% Correct answer.
  3. 60%
  4. 67%

Explanation

The Carnot efficiency is 1 − T_c/T_h, using absolute temperatures, so 1 − 300/500 = 0.40, or 40%. No engine working between these two reservoirs can exceed this value.

Question 24Physics

A parallel-plate capacitor is charged and then disconnected from the battery. The plate separation is then doubled. How do the electric field between the plates and the stored energy change?

  1. Field halves; energy halves
  2. Field doubles; energy doubles
  3. Field unchanged; energy doubles Correct answer.
  4. Field unchanged; energy halves

Explanation

With the battery removed the charge stays fixed, and the field E = σ/ε₀ depends only on surface charge density, so it is unchanged. Capacitance halves when separation doubles, and energy Q²/(2C) therefore doubles.

Question 25Physics

A particle of mass m is confined in an infinite one-dimensional potential well of width L. What is the energy of the first excited state?

  1. h²/(4mL²)
  2. h²/(2mL²) Correct answer.
  3. h²/(8mL²)
  4. 4h²/(8mL²)

Explanation

The allowed energies are E_n = n²h²/(8mL²), with n = 1, 2, 3, … for a particle in an infinite well. The first excited state has n = 2, giving E₂ = 4h²/(8mL²) = h²/(2mL²).

Question 26Physics

A ball is thrown vertically upward with a speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, what is the greatest height reached above the point of release?

  1. 10 m
  2. 2 m
  3. 40 m
  4. 20 m Correct answer.

Explanation

At the highest point the velocity is zero, so using v² = u² − 2gh with v = 0 gives h = u²/(2g). Substituting u = 20 m/s and g = 10 m/s² gives h = 400/20 = 20 m. The time to rise is 2 s, but height depends on the square of the initial speed.

Question 27Physics

A stone is dropped from rest and falls freely for 3 s. Taking g = 10 m/s², how far does it fall?

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

Explanation

For free fall from rest the distance is s = ½gt². With g = 10 m/s² and t = 3 s, s = ½ × 10 × 9 = 45 m. The velocity grows linearly with time, so the average speed is half the final speed of 30 m/s.

Question 28Physics

A force of 12 N acts on a body of mass 3 kg that is free to move on a frictionless horizontal surface. What is the acceleration of the body?

  1. 4 m/s² Correct answer.
  2. 0.25 m/s²
  3. 36 m/s²
  4. 9 m/s²

Explanation

Newton's second law states that the net force equals mass times acceleration, so a = F/m. Substituting F = 12 N and m = 3 kg gives a = 4 m/s². The acceleration is in the same direction as the applied force.

Question 29Physics

Which quantity is a scalar?

  1. Electric potential Correct answer.
  2. Electric field intensity
  3. Torque
  4. Linear momentum

Explanation

A scalar is fully specified by magnitude alone, and electric potential (volts) has no direction. Electric field, momentum and torque each require a direction for complete description and are vectors. Torque in particular is a vector given by the cross product of position and force.

Question 30Physics

A body moves in a circle of radius 2 m at a constant speed of 6 m/s. What is the magnitude of its centripetal acceleration?

  1. 18 m/s² Correct answer.
  2. 72 m/s²
  3. 3 m/s²
  4. 12 m/s²

Explanation

Centripetal acceleration has magnitude v²/r for uniform circular motion. Substituting v = 6 m/s and r = 2 m gives 36/2 = 18 m/s², directed toward the centre of the circle. The speed is constant but the velocity changes because its direction changes.

Question 31Physics

The work function of a metal surface is 2.0 eV. Light of photon energy 3.5 eV falls on it. What is the maximum kinetic energy of the emitted photoelectrons?

  1. 1.5 eV Correct answer.
  2. 0.57 eV
  3. 7.0 eV
  4. 5.5 eV

Explanation

Einstein's photoelectric equation gives maximum kinetic energy as photon energy minus work function. Here 3.5 eV − 2.0 eV = 1.5 eV. Emission occurs only because the photon energy exceeds the work function.

Question 32Physics

Which statement about the speed of sound in gases is correct?

  1. It decreases as the molar mass of the gas increases at fixed temperature.
  2. It increases with the square root of absolute temperature at constant molecular mass. Correct answer.
  3. It is independent of temperature.
  4. It increases in direct proportion to pressure at constant temperature.

Explanation

For an ideal gas the speed of sound is √(γRT/M), so at fixed molar mass it varies as the square root of absolute temperature. Changing pressure alone at constant temperature does not change the density ratio and hence leaves the speed unchanged. Lighter gases carry sound faster, not slower.

Question 33Physics

A wire of resistance 10 Ω is stretched uniformly so that its length is doubled while its volume stays constant. What is its new resistance?

  1. 40 Ω Correct answer.
  2. 5 Ω
  3. 10 Ω
  4. 20 Ω

Explanation

Stretching at constant volume doubles the length and halves the cross-sectional area. Since R = ρL/A, doubling L and halving A multiplies the resistance by four, giving 40 Ω. The resistivity itself is unchanged because the material is the same.

Question 34Physics

A block of mass 5 kg rests on a rough horizontal floor with coefficient of static friction 0.4. Taking g = 10 m/s², what is the minimum horizontal force needed to just start it moving?

  1. 12.5 N
  2. 20 N Correct answer.
  3. 50 N
  4. 2 N

Explanation

The limiting static friction equals μ times the normal reaction, and on a horizontal floor the normal reaction equals the weight. Thus f = 0.4 × 5 × 10 = 20 N, which is the minimum applied force to overcome it. Once motion begins, kinetic friction, usually smaller, acts.

Question 35Physics

Two capacitors of 2 μF and 3 μF are connected in series across a 10 V battery. What is the charge stored on each capacitor?

  1. 20 μC
  2. 12 μC Correct answer.
  3. 5 μC
  4. 50 μC

Explanation

The series equivalent capacitance is (2×3)/(2+3) = 1.2 μF. In series the charge is the same on both capacitors and equals CV = 1.2 μF × 10 V = 12 μC. The voltages divide as 6 V and 4 V across them.

Question 36Physics

A body of weight W is suspended by two light strings that each make an angle of 30° with the vertical. What is the tension in each string?

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

Explanation

By symmetry the two tensions are equal, and their vertical components must balance the weight. Each contributes T cos30°, so 2T cos30° = W, giving T = W/(2cos30°) = W/√3. The horizontal components cancel because the angles are equal.

Question 37Physics

An ideal gas is compressed adiabatically. Which combination correctly describes the changes?

  1. Temperature rises and internal energy increases Correct answer.
  2. Temperature rises while internal energy stays constant
  3. Temperature falls and internal energy decreases
  4. Temperature stays constant while work is done

Explanation

In an adiabatic process no heat is exchanged, so work done on the gas raises its internal energy. For an ideal gas internal energy depends only on temperature, so compression adiabatically heats the gas. This is why a bicycle pump barrel warms during rapid compression.

Question 38Physics

A travelling wave on a string is described by y = 0.02 sin(4πx − 200πt), with all quantities in SI units. What is the speed of the wave?

  1. 4 m/s
  2. 800 m/s
  3. 0.02 m/s
  4. 50 m/s Correct answer.

Explanation

Comparing with y = A sin(kx − ωt) gives wave number k = 4π rad/m and angular frequency ω = 200π rad/s. The speed is ω/k = 200π/4π = 50 m/s. The amplitude 0.02 m does not affect the propagation speed.

Question 39Physics

A step-down transformer has 1000 turns in the primary and 200 turns in the secondary. If the primary is connected to a 220 V ac supply, what is the secondary voltage, assuming ideal coupling?

  1. 22 V
  2. 44 V Correct answer.
  3. 1100 V
  4. 220 V

Explanation

For an ideal transformer the voltage ratio equals the turns ratio, Vs/Vp = Ns/Np. Thus Vs = 220 × (200/1000) = 44 V. The current in the secondary rises in the same proportion that the voltage falls.

Question 40Physics

A ray of light strikes the surface of a transparent medium of refractive index √3 from air at an angle of incidence of 60°. What is the angle of refraction?

  1. 60°
  2. 45°
  3. 30° Correct answer.
  4. 90°

Explanation

Snell's law gives sin r = sin i / n for incidence from air. Here sin60° = 0.866, so sin r = 0.866/1.732 = 0.5, giving r = 30°. The ray bends toward the normal because the second medium is optically denser.

Question 41Physics

A charged particle moves in a circular path in a uniform magnetic field with its velocity perpendicular to the field. If the speed is doubled while the field stays the same, how does the radius of the path change?

  1. It becomes four times larger
  2. It doubles Correct answer.
  3. It stays the same
  4. It halves

Explanation

The magnetic force supplies the centripetal force, so qvB = mv²/r and r = mv/(qB). The radius is directly proportional to speed for a given particle and field. Doubling the speed therefore doubles the radius, while the period of revolution stays unchanged.

Question 42Physics

The de Broglie wavelength of an electron is 0.5 nm. What is the magnitude of its momentum? (Take h = 6.6 × 10⁻³⁴ J s.)

  1. 1.32 × 10⁻²⁴ kg m/s Correct answer.
  2. 3.3 × 10⁻²⁵ kg m/s
  3. 6.6 × 10⁻³⁴ kg m/s
  4. 1.32 × 10⁻²⁵ kg m/s

Explanation

The de Broglie relation states that wavelength equals Planck's constant divided by momentum, so p = h/λ. Substituting h = 6.6 × 10⁻³⁴ J s and λ = 0.5 × 10⁻⁹ m gives p = 1.32 × 10⁻²⁴ kg m/s. This momentum corresponds to an electron speed far below that of light.

Question 43Physics

In a nuclear reaction, a stationary nucleus of mass number 236 splits into two fragments of mass numbers 100 and 132, together with four neutrons. Which conservation law explains why the total mass of the products is slightly less than the original mass?

  1. Conservation of charge only
  2. Conservation of nucleon number only
  3. Conservation of mass-energy Correct answer.
  4. Conservation of momentum only

Explanation

Mass-energy equivalence means the missing mass appears as kinetic energy of the fragments and neutrons. Momentum and nucleon number are also conserved, but they do not explain the mass deficit. Only the mass-energy relation E = mc² accounts for the released energy.

Question 44Physics

A body of mass 2 kg moving at 3 m/s collides elastically head-on with a stationary body of mass 1 kg. What is the velocity of the 2 kg body immediately after the collision?

  1. 0 m/s
  2. 3 m/s in the original direction
  3. −3 m/s
  4. 1 m/s in the original direction Correct answer.

Explanation

For a head-on elastic collision the final velocity of the projectile is ((m1 − m2)/(m1 + m2))u1. With m1 = 2 kg, m2 = 1 kg and u1 = 3 m/s, this gives (1/3) × 3 = 1 m/s forward. The lighter target moves off at 4 m/s in the same direction.

Question 45Physics

A body executes simple harmonic motion with amplitude 5 cm and angular frequency 4 rad/s. What is its maximum speed?

  1. 1.25 m/s
  2. 0.20 m/s Correct answer.
  3. 0.80 m/s
  4. 20 m/s

Explanation

In simple harmonic motion the maximum speed is the product of amplitude and angular frequency, v = Aω. Converting the amplitude to 0.05 m and multiplying by 4 rad/s gives 0.20 m/s. This maximum occurs as the body passes through the equilibrium position.

Question 46Physics

Two coherent sources emit waves of equal amplitude. At a point where the path difference is half a wavelength, what is the resultant intensity compared with the intensity of a single wave?

  1. Equal to the single-wave intensity
  2. Twice the single-wave intensity
  3. Four times the single-wave intensity
  4. Zero Correct answer.

Explanation

A path difference of half a wavelength corresponds to a phase difference of π radians. The two waves then arrive exactly out of phase and cancel, giving zero resultant amplitude and hence zero intensity. Complete cancellation requires equal amplitudes and stable coherence.

Question 47Physics

A 4 Ω resistor and a 6 Ω resistor are connected in series across a 12 V battery of negligible internal resistance. What is the power dissipated in the 6 Ω resistor?

  1. 3.84 W
  2. 24 W
  3. 14.4 W
  4. 8.64 W Correct answer.

Explanation

The series current is 12 V divided by the total resistance of 10 Ω, giving 1.2 A. Power in the 6 Ω resistor is I²R = 1.44 × 6 = 8.64 W. The 4 Ω resistor dissipates the remaining 5.76 W of the total 14.4 W.

Question 48Physics

A satellite orbits a planet in a circular orbit of radius r. Another satellite has a circular orbit of radius 4r around the same planet. What is the ratio of the orbital speed of the first satellite to that of the second?

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

Explanation

For a circular orbit the gravitational force provides the centripetal force, giving v = √(GM/r). Speed therefore varies as the inverse square root of orbital radius. Since the radius increases fourfold, the speed falls by a factor of two, so the ratio is 2 : 1.

Question 49Physics

A uniform rod of length L is pivoted about one end and released from rest in a horizontal position. What is the angular speed of the rod when it becomes vertical?

  1. √(3g/L) Correct answer.
  2. √(2g/L)
  3. √(6g/L)
  4. √(g/L)

Explanation

Energy conservation gives ½Iω² = Mg(L/2), where the centre of mass falls a distance L/2. With I = ML²/3 about the end, this yields ω² = 3g/L, so ω = √(3g/L). Treating the rod as a point mass at its end would give the wrong factor.

Question 50Physics

A charged particle of charge q and mass m moves with speed v in a uniform magnetic field B, its velocity making an angle of 60° with the field. What is the pitch of the resulting helical path?

  1. 2πmv/(qB)
  2. πmv/(qB) Correct answer.
  3. πmv/(2qB)
  4. √3πmv/(qB)

Explanation

The velocity component parallel to the field is v cos60° = v/2, which remains constant and carries the particle along the field. The perpendicular component sets the cyclotron period T = 2πm/(qB). The pitch is the product, giving (v/2) × 2πm/(qB) = πmv/(qB).