JAMB Physics 1999

28 reviewed questions with answers and explanations.

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Question 5

A rigid solid with base PQ rests on a slope, with enough friction to prevent sliding and no external support. G is its centre of gravity. Which statement describes when gravity makes it tip?

  1. It tips if the vertical line through G falls outside its base of support
  2. It tips if the vertical line through G lies inside its base
  3. It does not tip if the vertical line through G lies outside its base
  4. It can never tip
Answer and explanation

A: It tips if the vertical line through G falls outside its base of support

If the vertical line of weight falls outside the base, gravity produces a turning moment about the downhill edge that tips the solid. Inside the base, a supporting reaction can balance its weight.

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Question 6

Two bodies have masses in the ratio 3:1 and accelerations in the ratio 2:9, respectively. Find the ratio of the resultant forces acting on them.

  1. 1 : 4
  2. 2 : 1
  3. 2 : 3
  4. 2 : 5.
Answer and explanation

C: 2 : 3

Newton’s second law gives F₁/F₂ =(m₁/m₂)(a₁/a₂) =3 ×2/9 =2/3. The forces therefore have ratio 2:3.

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Question 7

A vehicle’s velocity-time graph consists of straight segments joining (0 s,0 m/s), (20 s,80 m/s), (50 s,80 m/s) and (90 s,0 m/s). Find its acceleration during the first segment and retardation magnitude during the last.

  1. 8 m/s², 4 m/s²
  2. 4 m/s², 8 m/s²
  3. 4 m/s², 2 m/s²
  4. 2 m/s², 4 m/s²
Answer and explanation

C: 4 m/s², 2 m/s²

The rising slope is (80 −0)/(20 −0) =4 m/s². The falling slope is (0 −80)/(90 −50) =−2 m/s², so the retardation magnitude is 2 m/s².

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Question 9

The inner diameter of a small test tube can be measured accurately using a

  1. Ordinary outside micrometer screw gauge
  2. Pair of dividers
  3. Metre rule
  4. Vernier calipers with inside jaws
Answer and explanation

D: Vernier calipers with inside jaws

The inside jaws of vernier calipers can contact opposite inner walls of the tube and measure the separation directly. An ordinary outside micrometer cannot measure that internal diameter.

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Question 12

A lift pump has valve P in its moving piston and inlet valve Q at the bottom of the cylinder. Both admit upward flow. During the downward stroke of the piston, which valves are open?

  1. Both valves are open
  2. P is open while Q is closed
  3. P is closed while Q is open
  4. Both valves are closed.
Answer and explanation

B: P is open while Q is closed

On the downstroke, water pressure below the piston closes the inlet valve Q and opens the piston valve P. Water passes upward through the piston instead of returning down the inlet.

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Question 14

Within the elastic range, a wire under stress 10⁷ Pa stretches from 10.00 cm to 10.05 cm. Find its Young’s modulus.

  1. 5.0 ×10⁴ Pa
  2. 5.0 ×10⁵ Pa
  3. 2.0 ×10⁸ Pa
  4. 2.0 ×10⁹ Pa
Answer and explanation

D: 2.0 ×10⁹ Pa

The strain is (10.05 −10.00)/10.00 =0.005. Young’s modulus is stress divided by strain: E =10⁷/0.005 =2.0 ×10⁹ Pa.

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Question 16

For boiling and a dilute aqueous solution with a nonvolatile solute, which statements are correct? I. A liquid boils when its saturated vapour pressure equals external pressure. II. Dissolving the solute raises water’s boiling point. III. Increasing external pressure raises the boiling point. IV. Dissolving the solute lowers water’s boiling point.

  1. I, II and III
  2. I, II, III and IV
  3. I, II and IV
  4. II, III and IV.
Answer and explanation

A: I, II and III

Boiling occurs when saturated vapour pressure reaches the external pressure. Raising external pressure raises boiling temperature. A nonvolatile solute lowers solvent vapour pressure and raises the solution’s boiling point.

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Question 17

As the temperature of a pure liquid such as water rises while it remains liquid, its surface tension generally

  1. Decreases
  2. Increases
  3. Remains constant
  4. Increase then decreases.
Answer and explanation

A: Decreases

For a pure liquid such as water, surface tension generally decreases as temperature rises. Greater thermal motion reduces the free-energy cost per unit area of forming its liquid surface.

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Question 21

A sound wave passes from colder air into hotter air of the same composition across a stationary boundary. Its wavelength

  1. Increases
  2. Decreases
  3. Decreases then increases
  4. Remains constant
Answer and explanation

A: Increases

Sound travels faster in hotter air of the same composition. Its frequency remains fixed by the source across a stationary boundary, so λ =v/f increases when the speed increases.

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Question 23

A wave is described in SI units by y =0.25 ×10⁻³ sin(500 t −0.025 x). Find its angular frequency.

  1. 0.25 ×10⁻³ rad/s
  2. 0.25 ×10⁻¹ rad/s
  3. 5.00 ×10² rad/s
  4. 2.50 ×10² rad/s
Answer and explanation

C: 5.00 ×10² rad/s

Compare y =A sin(ωt −kx) with the given equation. The coefficient of time in the phase is the angular frequency, so ω =500 rad/s =5.00 ×10² rad/s.

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Question 24

A 2 kg copper block at 100°C is placed on ice at 0°C without heat loss. Find the mass of ice melted. Take copper’s specific heat capacity as 400 J/(kg·K) and ice’s latent heat of fusion as 3.3 ×10⁵ J/kg.

  1. 8/33 kg
  2. 33/80 kg
  3. 80/33 kg
  4. 33/8 kg
Answer and explanation

A: 8/33 kg

The copper releases Q =mcΔT =2 ×400 ×100 =80,000 J while cooling to 0°C. Melting needs mᵢL =Q, so mᵢ =80,000/330,000 =8/33 kg.

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Question 25

A spatial snapshot of a transverse electromagnetic wave contains three complete cycles over 0.30 m, from an upward zero crossing to the third following upward zero crossing. Its speed is 3.0 ×10⁸ m/s. Find its frequency.

  1. 3.0 ×10⁷ Hz
  2. 90 ×10⁷ Hz
  3. 1.0 ×10⁹ Hz
  4. 3.0 ×10⁹ Hz
Answer and explanation

D: 3.0 ×10⁹ Hz

Three complete cycles occupy 0.30 m, so the wavelength is 0.30/3 =0.10 m. Hence f =v/λ =(3.0 ×10⁸)/0.10 =3.0 ×10⁹ Hz.

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Question 27

The ends of a 0.02 m length of copper are maintained at 20°C and 80°C. Find the magnitude of the temperature gradient.

  1. 3.0 ×10² K/m
  2. 3.0 ×10³ K/m
  3. 5.0 ×10³ K/m
  4. 3.0 ×10⁴ K/m
Answer and explanation

B: 3.0 ×10³ K/m

The temperature difference is 80 −20 =60 K. The magnitude of the gradient is ΔT/Δx =60/0.02 =3000 K/m =3.0 ×10³ K/m.

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Question 29

Four identical cells, each of emf 1.5 V and internal resistance 4 Ω, are connected in parallel with matching polarities. Find the effective emf and internal resistance.

  1. 6.0 V, 16 Ω
  2. 6.0 V, 1 Ω
  3. 1.5 V, 4 Ω
  4. 1.5 V, 1 Ω
Answer and explanation

D: 1.5 V, 1 Ω

Identical cells connected in parallel with matching polarities retain the emf of one cell, 1.5 V. Their internal resistances act in parallel, giving r =4/4 =1 Ω.

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Question 31

An astronomical telescope is said to be in normal adjustment when the

  1. Eye is accommodated
  2. Focal length of objective lens is longer than that of eye piece
  3. Final image is at the near point of eye
  4. Final image is at infinity.
Answer and explanation

D: Final image is at infinity.

Normal adjustment places the intermediate image at the eyepiece’s focal plane, so rays from each image point emerge parallel. The final image is therefore at infinity and a relaxed eye can view it.

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Question 32

Hardened steel is more suitable than soft iron for a permanent magnet because it

  1. Is easily demagnetized by vigorous shaking
  2. Is an alloy of many metals
  3. Is easily magnetized by alternating current through one cycle
  4. Retains magnetism more strongly
Answer and explanation

D: Retains magnetism more strongly

Hardened steel retains substantial magnetization after the magnetizing field is removed and resists demagnetization. Soft iron is easier to magnetize and demagnetize, making it better suited to temporary magnetic cores.

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Question 33

Two right-angle prisms are vertically separated. Light travels horizontally into the upper prism, turns 90° downward, then turns 90° in the lower prism and emerges horizontally in its original direction at a lower level. This is the basic prism arrangement in a

  1. Binocular
  2. Spectrometer
  3. Periscope
  4. Projector
Answer and explanation

C: Periscope

Two right-angle prisms can reflect a light path down from a higher viewing point and then horizontally to a lower observer. This displaced viewing path is the basic arrangement of a prism periscope.

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Question 34

Light travels from air into glass. Its speeds are 3.0 ×10⁸ m/s in air and 2.0 ×10⁸ m/s in glass. If the angle of refraction is 30°, find the sine of the angle of incidence.

  1. 0.33
  2. 0.50
  3. 0.67
  4. 0.75
Answer and explanation

D: 0.75

Snell’s law gives sin i/sin r =v_air/v_glass =3/2. With r =30° and sin 30° =0.5, sin i =(3/2) ×0.5 =0.75.

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Question 35

A sinusoidal source supplies one series loop containing an ideal inductor L and a resistor R. Their RMS voltages are V_L =8 V and V_R =6 V. Find the source RMS voltage.

  1. 2 V
  2. 10 V
  3. 14 V
  4. 48 V
Answer and explanation

B: 10 V

Resistor voltage is in phase with current, while ideal-inductor voltage leads current by 90°. The supply RMS voltage is their phasor sum: √(6² +8²) =10 V.

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Question 36

A transformer core is made from thin insulated metal laminations mainly to

  1. Increase the heat produced by increasing the eddy current
  2. Increase the heat produced by reducing the eddy current
  3. Reduce the heat produced by increasing the eddy current
  4. Reduce the heat produced by reducing the eddy current.
Answer and explanation

D: Reduce the heat produced by reducing the eddy current.

Insulated laminations interrupt large circulating paths in the metal core. This reduces eddy currents and their resistive heating, improving transformer efficiency.

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Question 37

In Fleming’s right-hand rule, the thumb, the forefinger and the middle finger if held mutually at right angles represent respectively, the

  1. Motion, magnetic field and induced current
  2. Induced current, motion and magnetic field
  3. Magnetic field, induced current and motion
  4. Induced current, magnetic field and motion
Answer and explanation

A: Motion, magnetic field and induced current

For Fleming’s generator right-hand rule, the thumb indicates conductor motion, the first finger the magnetic field, and the second finger the induced conventional current. The three directions are mutually perpendicular.

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Question 38

A 2 μF capacitor and a 3 μF capacitor are connected in parallel across 100 V, with their marked positive plates at the same terminal. Find their total stored energy.

  1. 3.0 ×10⁴ J
  2. 3.0 ×10² J
  3. 2.5 ×10⁻² J
  4. 6.0 ×10⁻³ J
Answer and explanation

C: 2.5 ×10⁻² J

Both parallel capacitors have 100 V across them. Their total stored energy is ½(C₁ +C₂)V² =½(2 +3) ×10⁻⁶ ×100² =0.025 J.

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Question 39

At what frequency would a 10 H inductor have a reactance of 2000 ohms?

  1. π/200 Hz
  2. π/100 Hz
  3. 100/π Hz
  4. 100π Hz
Answer and explanation

C: 100/π Hz

Inductive reactance is X_L =2πfL. Rearranging gives f =2000/(2π ×10) =100/π Hz, approximately 31.8 Hz.

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Question 42

Two resistors R₁ and R₂ are connected in separate parallel branches across a cell of emf E and zero internal resistance. If their powers are P₁ and P₂, respectively, find P₁/P₂.

  1. R₂/R₁
  2. R₁/R₂
  3. (R₁ + R₂)/R₁
  4. (R₁ + R₂)/R₂
Answer and explanation

A: R₂/R₁

The resistors are in parallel, so each has the cell voltage E across it. Since P =V²/R, the ratio is P₁/P₂ =(E²/R₁)/(E²/R₂) =R₂/R₁.

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Question 46

In an ordinary crystalline semiconductor at room temperature, the mobile carriers of electric current are

  1. Electrons only
  2. Electrons and holes
  3. Holes only
  4. Electrons and ions
Answer and explanation

B: Electrons and holes

Conduction-band electrons and mobile holes in the valence band both carry current in ordinary semiconductors. A hole represents a missing valence electron and behaves as a positive charge carrier.

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Question 47

Find the speed of a particle with mass 10⁻²⁷ kg and de Broglie wavelength 10⁻⁸ m. Use h =6.63 ×10⁻³⁴ J·s.

  1. 6.63 m/s
  2. 66.30 m/s
  3. 663.00 m/s
  4. 6630.00 m/s
Answer and explanation

B: 66.30 m/s

De Broglie’s relation is λ =h/p. At this low speed p =mv, so v =h/(mλ) =(6.63 ×10⁻³⁴)/(10⁻²⁷ ×10⁻⁸) =66.3 m/s.

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Question 48

In a series circuit containing R and ideal L and C at resonance, the RMS voltages across R and L are 30 V and 40 V. What is the RMS voltage across C?

  1. 30 V
  2. 40 V
  3. 50 V
  4. 70 V
Answer and explanation

B: 40 V

At series resonance, X_L =X_C. The same current passes through both components, so their voltage magnitudes are equal and opposite in phase. Thus the capacitor voltage is 40 V.

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Question 49

In nuclear gamma emission, the radiation is produced when

  1. Fast electrons are abruptly stopped in a metal
  2. An excited nucleus changes to a lower energy state
  3. Electrons change energy levels within an atom
  4. Electrons are deflected by a strong magnetic field
Answer and explanation

B: An excited nucleus changes to a lower energy state

In nuclear gamma emission, an excited nucleus changes to a lower energy state and releases the energy difference as a photon. This is distinct from transitions among atomic electron energy levels.

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