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Fukushima Entrance Science practice questions

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Question 1Physics

A block slides down a frictionless incline of height h starting from rest. Which expression gives its speed at the bottom?

  1. v = √(gh)
  2. v = gh
  3. v = 2gh
  4. v = √(2gh) Correct answer.

Explanation

On a frictionless incline, mechanical energy is conserved, so the potential energy mgh converts entirely into kinetic energy ½mv². Setting mgh = ½mv² and solving gives v = √(2gh), independent of the incline angle.

Question 2Physics

An object moves in a circle of radius r at constant speed v. What is the magnitude of its centripetal acceleration?

  1. v/r
  2. v²r
  3. vr
  4. v²/r Correct answer.

Explanation

Uniform circular motion has an acceleration directed toward the center with magnitude v²/r. This follows from the changing direction of the velocity vector, and it can also be written ω²r using angular speed ω = v/r.

Question 3Physics

A 2 kg object accelerates at 3 m/s². What net force acts on it?

  1. 1.5 N
  2. 0.67 N
  3. 5 N
  4. 6 N Correct answer.

Explanation

Newton's second law states F = ma. Substituting m = 2 kg and a = 3 m/s² gives F = 6 N, and the force points in the same direction as the acceleration.

Question 4Physics

Which quantity is a scalar?

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

Explanation

A scalar has magnitude only, while a vector has both magnitude and direction. Speed is the magnitude of velocity, so it carries no direction and is a scalar, whereas velocity, acceleration, and displacement are all vectors.

Question 5Physics

What is the SI unit of electrical resistance?

  1. Ohm Correct answer.
  2. Volt
  3. Watt
  4. Ampere

Explanation

Resistance is measured in ohms (Ω), defined as one volt per ampere. The volt measures potential difference, the ampere measures current, and the watt measures power.

Question 6Physics

A wave has frequency 50 Hz and wavelength 4 m. What is its speed?

  1. 54 m/s
  2. 0.08 m/s
  3. 12.5 m/s
  4. 200 m/s Correct answer.

Explanation

The wave speed equation is v = fλ. Multiplying the frequency 50 Hz by the wavelength 4 m gives v = 200 m/s, which is the speed at which the wave crests travel through the medium.

Question 7Physics

Two point charges are moved twice as far apart while their charges stay the same. How does the electrostatic force between them change?

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

Explanation

Coulomb's law states that the force is inversely proportional to the square of the separation. Doubling the distance multiplies the force by 1/2² = 1/4, so it becomes one quarter as large.

Question 8Physics

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

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

Explanation

The magnetic force is given by F = qv × B, a cross product that is perpendicular to both the velocity and the field. This is why the force does no work on the charge and changes only the direction of motion.

Question 9Physics

A 5 kg mass hangs at rest from a single vertical rope. Taking g = 10 m/s², what is the tension in the rope?

  1. 5 N
  2. 50 N Correct answer.
  3. 500 N
  4. 0.5 N

Explanation

Because the mass is in equilibrium, the upward tension balances the downward weight mg. With m = 5 kg and g = 10 m/s², the weight is 50 N, so the tension is also 50 N.

Question 10Physics

A projectile is launched at an angle above the horizontal on level ground, ignoring air resistance. At the highest point of its path, what is true?

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

Explanation

Horizontal and vertical motions are independent. Gravity acts only vertically, so the horizontal velocity stays constant while the vertical velocity decreases to zero at the apex, after which it reverses direction.

Question 11Physics

A 1200 kg car moving at 10 m/s collides and sticks to a stationary 800 kg car. What is their common speed just after the collision?

  1. 4 m/s
  2. 6 m/s Correct answer.
  3. 5 m/s
  4. 10 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved: m₁v₁ = (m₁ + m₂)v. Thus 1200 × 10 = 2000 × v, giving v = 6 m/s, while kinetic energy is not conserved.

Question 12Physics

A force of 20 N is applied at 60° to the horizontal to drag a box along a floor. What is the horizontal component of the force?

  1. 20 N
  2. 17.3 N
  3. 34.6 N
  4. 10 N Correct answer.

Explanation

The horizontal component is F cos θ. With F = 20 N and θ = 60°, cos 60° = 0.5, so the component is 10 N. The vertical component would be F sin θ = 17.3 N.

Question 13Physics

An ideal gas is held at constant temperature while its volume is halved. What happens to its pressure?

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

Explanation

Boyle's law states that at constant temperature, pressure and volume are inversely proportional (PV = constant). Halving the volume therefore doubles the pressure.

Question 14Physics

A 2 kg block at 80 °C is placed in 2 kg of water at 20 °C, and the system reaches thermal equilibrium with no heat loss. If the specific heat of the block is half that of water, what is the final temperature?

  1. 30 °C
  2. 60 °C
  3. 40 °C Correct answer.
  4. 50 °C

Explanation

Heat lost by the block equals heat gained by the water: m c (80 − T) = m (2c)(T − 20), where the block's specific heat is c and the water's is 2c. Solving gives 80 − T = 2(T − 20), so T = 40 °C.

Question 15Physics

A 4 Ω and a 6 Ω resistor are connected in parallel across a 12 V source. What is the total current drawn from the source?

  1. 3 A
  2. 1.2 A
  3. 5 A Correct answer.
  4. 2 A

Explanation

The equivalent resistance of 4 Ω and 6 Ω in parallel is (4 × 6)/(4 + 6) = 2.4 Ω. The total current is V/R = 12/2.4 = 5 A, which also equals the sum of branch currents 3 A and 2 A.

Question 16Physics

A convex lens has a focal length of 10 cm. An object is placed 30 cm in front of it. Where is the image formed?

  1. 15 cm on the opposite side of the lens Correct answer.
  2. 10 cm on the opposite side
  3. 7.5 cm on the opposite side
  4. 30 cm on the same side as the object

Explanation

The thin-lens equation gives 1/f = 1/do + 1/di, so 1/di = 1/10 − 1/30 = 1/15. Thus di = 15 cm, a real image on the far side of the lens, inverted and reduced.

Question 17Physics

Light of wavelength 500 nm passes through a single slit of width 0.1 mm. Approximately what is the angular width of the central diffraction maximum, measured between the first minima?

  1. 2 × 10⁻² rad
  2. 5 × 10⁻³ rad
  3. 1 × 10⁻² rad Correct answer.
  4. 1 × 10⁻³ rad

Explanation

The first minima of a single slit occur at sin θ = λ/a. Here λ/a = 500 × 10⁻⁹ / 1 × 10⁻⁴ = 5 × 10⁻³, so each minimum is at about 5 × 10⁻³ rad and the full central maximum is roughly 1 × 10⁻² rad wide.

Question 18Physics

In the photoelectric effect, increasing the intensity of incident light above the threshold frequency increases which quantity?

  1. The threshold frequency of the metal
  2. The number of emitted electrons per second Correct answer.
  3. The work function of the metal
  4. The maximum kinetic energy of the emitted electrons

Explanation

Each photon ejects at most one electron, so higher intensity means more photons per second and thus more photoelectrons. The maximum kinetic energy depends on photon frequency through hf = φ + Kmax, not on intensity, and the work function is a property of the metal.

Question 19Physics

A radioactive sample has a half-life of 8 days. What fraction of the original nuclei remains after 24 days?

  1. 1/24
  2. 1/8 Correct answer.
  3. 1/3
  4. 1/6

Explanation

After 24 days, three half-lives have elapsed since 24/8 = 3. Each half-life halves the remaining nuclei, so the fraction is (1/2)³ = 1/8.

Question 20Physics

A satellite orbits Earth in a circular orbit. If its orbital radius is increased, what happens to its orbital speed?

  1. It increases
  2. It decreases Correct answer.
  3. It stays the same
  4. It becomes zero

Explanation

Setting gravitational force equal to centripetal force gives GMm/r² = mv²/r, so v = √(GM/r). The orbital speed therefore decreases as the radius increases, which is why distant satellites move more slowly.

Question 21Physics

A block of mass m is pulled up an incline at constant velocity by a force parallel to the incline, with coefficient of kinetic friction μ. If the incline angle is θ, what is the magnitude of the applied force?

  1. mg(sin θ + μ cos θ) Correct answer.
  2. mg cos θ
  3. mg μ sin θ
  4. mg(sin θ − μ cos θ)

Explanation

At constant velocity the net force is zero. The applied force must balance both the downhill component of weight, mg sin θ, and kinetic friction, μmg cos θ, giving F = mg(sin θ + μ cos θ).

Question 22Physics

A mass on a spring oscillates with period T. If the mass is replaced by one four times larger while the spring is unchanged, what is the new period?

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

Explanation

The period of a spring oscillator is T = 2π√(m/k), so it scales with the square root of mass. Quadrupling the mass multiplies the period by √4 = 2, giving 2T.

Question 23Physics

An ideal gas expands isothermally and reversibly from volume V to 2V at temperature T. Which statement about the heat absorbed Q and work done W by the gas is correct?

  1. Q = 0 and W = nRT ln 2
  2. Q = W = nRT
  3. Q = nRT ln 2 and W = 0
  4. Q = W = nRT ln 2 Correct answer.

Explanation

For an isothermal process the internal energy of an ideal gas is constant, so the first law gives Q = W. The reversible work is W = ∫(nRT/V)dV = nRT ln 2, so both heat absorbed and work done equal nRT ln 2.

Question 24Physics

Two coherent sources emit in phase at wavelength λ. At a point where the path difference is 1.5λ, what is observed?

  1. No interference pattern
  2. Destructive interference Correct answer.
  3. Constructive interference
  4. A polarization rotation

Explanation

Constructive interference occurs at path differences of whole multiples of λ, and destructive interference at odd half-multiples. A path difference of 1.5λ = (3/2)λ is an odd half-multiple, so the waves arrive out of phase and cancel.

Question 25Physics

A capacitor of capacitance C is charged to voltage V and then disconnected from the source. A dielectric of constant κ is inserted to fill the gap. What happens to the stored energy?

  1. It stays the same
  2. It increases by a factor of κ
  3. It decreases by a factor of κ²
  4. It decreases by a factor of κ Correct answer.

Explanation

With the source disconnected, charge Q is fixed. Inserting the dielectric multiplies capacitance by κ, and energy U = Q²/(2C) therefore falls by a factor of κ, the lost energy going into pulling the dielectric into the gap.

Question 26Physics

A body moves along a straight line with constant acceleration of 2 m/s² starting from rest. How far does it travel in the first 5 s?

  1. 25 m Correct answer.
  2. 50 m
  3. 10 m
  4. 5 m

Explanation

With zero initial velocity, displacement is s = ½at². Substituting a = 2 m/s² and t = 5 s gives s = ½ × 2 × 25 = 25 m. The velocity grows linearly, so the average speed over the interval is only half the final speed.

Question 27Physics

A ball is thrown vertically upward and returns to the thrower's hand. Ignoring air resistance, which quantity is zero at the highest point of the motion?

  1. Gravitational potential energy
  2. Vertical acceleration
  3. Vertical velocity Correct answer.
  4. Total mechanical energy

Explanation

At the top of the flight the ball momentarily stops rising before falling, so its vertical velocity passes through zero. Gravity continues to act throughout, so the acceleration remains g downward. Mechanical energy is conserved and potential energy is at its maximum there.

Question 28Physics

A skater spinning with arms outstretched pulls her arms in, reducing her moment of inertia. What happens to her angular velocity and angular momentum?

  1. Angular velocity decreases and angular momentum stays constant
  2. Angular velocity increases and angular momentum stays constant Correct answer.
  3. Both angular velocity and angular momentum increase
  4. Angular velocity stays constant and angular momentum increases

Explanation

No external torque acts about the vertical axis, so angular momentum L = Iω is conserved. When the moment of inertia I falls, ω must rise to keep the product constant. The skater therefore spins faster without gaining angular momentum.

Question 29Physics

A solid sphere and a hollow spherical shell of the same mass and radius roll without slipping down the same incline from rest. Which reaches the bottom first?

  1. The hollow shell
  2. The solid sphere Correct answer.
  3. Both arrive at the same time
  4. It depends on the incline angle

Explanation

Rolling bodies accelerate at g sinθ/(1 + I/mR²), so the smaller the moment-of-inertia factor the faster the descent. A solid sphere has I = 2/5 mR² while a hollow shell has I = 2/3 mR², so the solid sphere wins regardless of the incline angle.

Question 30Physics

A 3 kg object moving at 4 m/s collides head-on with a 1 kg object at rest, and the two stick together. What is the kinetic energy lost in the collision?

  1. 24 J
  2. 6 J Correct answer.
  3. 12 J
  4. 18 J

Explanation

Momentum conservation gives a common speed of (3 × 4)/4 = 3 m/s. Initial kinetic energy is ½ × 3 × 16 = 24 J and final energy is ½ × 4 × 9 = 18 J, so 6 J is lost. A perfectly inelastic collision always dissipates energy.

Question 31Physics

A crate slides at constant speed down a rough incline. Which statement about the forces on the crate is correct?

  1. The net force points down the incline
  2. Kinetic friction is greater than the component of gravity along the incline
  3. The normal force equals the weight of the crate
  4. The component of gravity along the incline equals the kinetic friction force Correct answer.

Explanation

Constant velocity means zero net force, so along the incline the downward gravity component balances friction. The normal force equals mg cosθ, not the full weight. A net force along the incline would produce acceleration, contradicting the constant speed.

Question 32Physics

An object of weight 20 N is fully submerged in water and displaces 3 litres of water. Taking the density of water as 1 kg/L and g = 10 m/s², what is the buoyant force?

  1. 30 N Correct answer.
  2. 10 N
  3. 3 N
  4. 20 N

Explanation

The displaced water has mass 3 kg, so the buoyant force is 3 × 10 = 30 N. This exceeds the 20 N weight, so the object would accelerate upward if released. Buoyancy depends on displaced volume, not on the object's own weight.

Question 33Physics

A hydraulic press has a small piston of area 5 cm² and a large piston of area 200 cm². If a force of 100 N is applied to the small piston, what force appears at the large piston (ideal fluid, no losses)?

  1. 2000 N
  2. 500 N
  3. 4000 N Correct answer.
  4. 100 N

Explanation

Pascal's principle gives equal pressure, so F₂ = F₁ × A₂/A₁ = 100 × 200/5 = 4000 N. The area ratio of 40 multiplies the applied force by 40. The large piston moves a correspondingly smaller distance.

Question 34Physics

A sound source moves toward a stationary observer. Compared with the emitted sound, the observed sound has which combination of properties?

  1. Higher frequency and shorter wavelength Correct answer.
  2. Lower frequency and shorter wavelength
  3. Higher frequency and longer wavelength
  4. Lower frequency and longer wavelength

Explanation

Approach compresses successive wavefronts, so the observer intercepts more of them per second and hears a higher frequency. Because the speed of sound in air is essentially fixed by the medium, the shorter wavelength accompanies the higher frequency via v = fλ.

Question 35Physics

A pipe closed at one end resonates at its fundamental frequency of 100 Hz. What is the frequency of the next resonance above the fundamental?

  1. 150 Hz
  2. 400 Hz
  3. 300 Hz Correct answer.
  4. 200 Hz

Explanation

A closed pipe supports only odd harmonics, with resonant frequencies f, 3f, 5f, and so on. The next resonance above 100 Hz is therefore the third harmonic at 300 Hz. The closed end must be a displacement node, which excludes even multiples.

Question 36Physics

Two identical resistors are first connected in series and then in parallel across the same battery. What is the ratio of the power dissipated in the series connection to that in the parallel connection?

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

Explanation

In series the resistance is 2R, giving power V²/2R; in parallel it is R/2, giving power 2V²/R. The ratio of series to parallel power is therefore (1/2)/(2) = 1/4. The parallel arrangement draws four times the total power.

Question 37Physics

A wire of resistance R is uniformly stretched so that its length doubles while its volume stays constant. What is its new resistance?

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

Explanation

Constant volume with doubled length halves the cross-sectional area. Since R = ρL/A, doubling L and halving A multiplies the resistance by 4. Stretching always raises resistance faster than the length alone would suggest.

Question 38Physics

A charged particle enters a uniform magnetic field with its velocity perpendicular to the field lines. What path does it follow?

  1. A helix of decreasing radius
  2. A circle of constant speed Correct answer.
  3. A parabola with increasing speed
  4. A straight line at constant speed

Explanation

The magnetic force is always perpendicular to velocity, so it changes direction but not speed. A constant-magnitude centripetal force at constant speed produces uniform circular motion. The radius is r = mv/(qB).

Question 39Physics

A straight wire carries a current of 5 A and lies perpendicular to a uniform magnetic field of 0.2 T. What is the magnitude of the force on a 0.5 m length of the wire?

  1. 0.5 N Correct answer.
  2. 0.1 N
  3. 2.0 N
  4. 5.0 N

Explanation

The force on a current-carrying wire is F = BIL sinθ, and here sinθ = 1. Substituting gives 0.2 × 5 × 0.5 = 0.5 N. The direction follows the right-hand rule, perpendicular to both the wire and the field.

Question 40Physics

Electromagnetic induction in a coil is best described by which statement?

  1. An emf is induced only when the coil carries a steady current
  2. An emf is induced only when the magnetic flux through the coil changes with time Correct answer.
  3. An emf is induced whenever a steady magnetic flux passes through the coil
  4. An emf is induced only when the coil is electrically grounded

Explanation

Faraday's law states that the induced emf equals the negative rate of change of magnetic flux linkage. A steady flux, however large, produces no emf. The flux can change through motion, a changing field, or a changing coil area.

Question 41Physics

An alternating voltage has a peak value of 141 V. What is its root-mean-square value, approximately?

  1. 141 V
  2. 100 V Correct answer.
  3. 71 V
  4. 200 V

Explanation

For a sinusoid, V_rms = V_peak/√2. Dividing 141 V by about 1.414 gives approximately 100 V. The rms value is the equivalent steady voltage that would dissipate the same average power in a resistor.

Question 42Physics

A point charge is enclosed by a spherical Gaussian surface. If the radius of the sphere is doubled while the charge stays inside, what happens to the total electric flux through the surface?

  1. It is halved
  2. It is doubled
  3. It stays the same Correct answer.
  4. It is quartered

Explanation

Gauss's law states that the total flux through a closed surface equals the enclosed charge divided by ε₀. It depends only on the enclosed charge, not on the size or shape of the surface. Doubling the radius changes the field strength at the surface but not the total flux.

Question 43Physics

Two identical capacitors are connected in series across a battery. Compared with one capacitor alone across the same battery, the total stored energy is which of the following?

  1. Four times as much
  2. Half as much Correct answer.
  3. Twice as much
  4. The same

Explanation

Series connection halves the equivalent capacitance to C/2. Stored energy is ½CV², so with the same voltage the energy is halved. The charge on each capacitor is also reduced compared with the single-capacitor case.

Question 44Physics

Which statement correctly describes the electric field inside a conductor in electrostatic equilibrium?

  1. The field is zero throughout the interior Correct answer.
  2. The field is strongest at the centre
  3. The field equals the field of a point charge at the centre
  4. The field points radially outward everywhere

Explanation

In electrostatic equilibrium, free charges redistribute until they experience no net force, so the interior field vanishes. Any excess charge resides on the surface. The surface field is perpendicular to the surface.

Question 45Physics

A gas undergoes an adiabatic compression. Which statement about the work done on the gas and its internal energy is correct?

  1. Work is done by the gas and its internal energy decreases
  2. Heat flows into the gas and the internal energy is unchanged
  3. Work is done on the gas and its internal energy increases Correct answer.
  4. No work is done and the internal energy is unchanged

Explanation

Adiabatic means no heat exchange, so the first law reduces to ΔU = W_on. Compressing the gas means positive work is done on it, raising its internal energy and temperature. This is why a bicycle pump barrel warms during rapid compression.

Question 46Physics

In a Carnot engine operating between reservoirs at 600 K and 300 K, what is the maximum theoretical efficiency?

  1. 50% Correct answer.
  2. 75%
  3. 25%
  4. 100%

Explanation

Carnot efficiency is 1 − T_cold/T_hot, using absolute temperatures. Here 1 − 300/600 = 0.5, or 50%. No real engine between these reservoirs can exceed this value.

Question 47Physics

An ideal gas is heated at constant volume. Which statement about the heat supplied is correct?

  1. The heat supplied equals the work done by the gas
  2. Half the heat becomes work and half raises the internal energy
  3. The internal energy stays constant while the pressure rises
  4. All the heat raises the internal energy because no work is done Correct answer.

Explanation

At constant volume no expansion work occurs, so the first law gives Q = ΔU. All the heat goes into raising the internal energy and hence the temperature. The pressure rises in proportion to the absolute temperature.

Question 48Physics

In a photoelectric experiment, the stopping potential is measured for light of a given frequency. If light of higher frequency but lower intensity is used, what happens?

  1. The stopping potential increases because the maximum kinetic energy of the electrons increases Correct answer.
  2. No electrons are emitted because the intensity is lower
  3. The stopping potential stays the same because intensity is lower
  4. The stopping potential decreases because fewer photons arrive

Explanation

Einstein's equation gives eV_stop = hf − φ, so the stopping potential depends on frequency and work function, not intensity. A higher frequency means more energetic photons and faster photoelectrons. Lower intensity only reduces the number of electrons per second.

Question 49Physics

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

  1. The proton Correct answer.
  2. Both have the same wavelength
  3. The electron
  4. It depends on the sign of the accelerating voltage

Explanation

After acceleration the kinetic energy equals eV for both particles, so momentum p = √(2meV) is larger for the heavier proton. Since λ = h/p, the larger momentum gives the shorter wavelength. Mass, not charge sign, sets the difference.

Question 50Physics

A nucleus undergoes alpha decay. How do its mass number and atomic number change?

  1. Mass number is unchanged and atomic number decreases by 2
  2. Mass number decreases by 4 and atomic number is unchanged
  3. Mass number decreases by 2 and atomic number decreases by 4
  4. Mass number decreases by 4 and atomic number decreases by 2 Correct answer.

Explanation

An alpha particle is a helium-4 nucleus with 2 protons and 2 neutrons. Emitting it removes 4 nucleons and 2 units of positive charge, so A falls by 4 and Z falls by 2. Beta decay, by contrast, leaves A unchanged.