45 questions. Try each one, then open the answer to check yourself and read the explanation.
Question 1
Gravitational Field
Which of the following statements is true of the law of universal gravitation?
A.Any two bodies attract each other with a force which is proportional to the difference of their masses.
B.Any two bodies attract each other with a force which is inversely proportional to the square of the distance between them
C.Any two bodies attract each other with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them
D.Any two bodies attract each other with a force which is directly proportional to the square of the distance between them
E.Any two bodies attract each other with a force which is proportional to the sum of their masses.
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Answer: C (Any two bodies attract each other with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them)
Explanation
Newton's law of gravitation: F = Gm1m2/r², proportional to the product of the masses and inversely proportional to the square of their separation. Option B states only half of the law.
Which of the following is true of an electrical charge?
A.Positive charge means deficit electrons
B.Negative charge means excess of electrons
C.Electric current means movement of electrons
D.All of the above
E.A and B only.
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Answer: D (All of the above)
Explanation
A body is positive when it has lost electrons and negative when it has gained extra electrons; in metal wires an electric current is a flow of electrons.
Which of the following statements are true in the structure of atoms?
A.The atoms of the different elements differ only in the number of protons and electrons
B.The number of protons equals the number of electrons
C.Atoms are constructed according to the plan of our solar system
D.All of the above
E.A and C only.
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Answer: B (The number of protons equals the number of electrons)
Explanation
A neutral atom has as many electrons as protons. Atoms also differ in their numbers of neutrons, and electrons do not move in planet-like orbits, so A and C are not correct.
A magnet is similar to a bipolar charged system in that
A.it consists of two opposite poles – the north and south poles
B.the earth's magnetic field has a south pole near the geographic north pole and a north pole near the geographic south pole
C.the force of attraction and repulsion between opposite and between like poles obeys a law identical in form to Coulomb's law for electrostatic charges
D.A and B only
E.A and C only
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Answer: E (A and C only)
Explanation
Like a pair of opposite charges, a magnet has two opposite poles, and the force between poles follows an inverse-square law of the same form as Coulomb's law. B is true about the earth but is not a likeness to a charged system.
In the study of Physics, temperature and heat are often confused with each other. Which of the following statements correctly defines these two elements?
A.Temperature is a measure of the average kinetic energy of the molecules of a substance
B.Heat is a measure of the total kinetic energy of the molecules in a system
C.Different materials require different amounts of heat to cause a given change in temperature
D.all of the above
E.A and B only.
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Answer: D (all of the above)
Explanation
Temperature measures the average kinetic energy of the molecules, heat relates to their total energy, and different materials have different specific heat capacities. All three are true.
A given quantity of heat increases the temperature of 150 grams of water from 9°C to 15°C and increases the temperature of an equal volume of oil weighing 100 grams from 9°C to 25°C. The ratio of the specific heat of oil to that of water is
A.0.36
B.0.46
C.0.56
D.0.76
E.0.86
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Answer: C (0.56)
Explanation
The same heat goes in: 150 × cw × 6 = 100 × co × 16. So co/cw = 900/1600 ≈ 0.56.
The diagram in the above figure shows the prism arrangement in a
A.microscope
B.stereoscope
C.projector
D.periscope
E.gyroscope
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Answer: D (periscope)
Explanation
Two right-angled prisms turn the light through 90° twice, so it comes out parallel to its original direction but at a different level: this is a prism periscope.
The water at the bottom of a waterfall is slightly warmer than that at the top because part of the
A.potential energy raises the water temperature
B.water absorbs latent heat from the atmosphere
C.kinetic energy is changed into internal energy
D.dropping mass of water increases the heat capacity
E.A and C above.
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Answer: C (kinetic energy is changed into internal energy)
Explanation
As the water falls its potential energy becomes kinetic energy; when it strikes the bottom, part of that kinetic energy becomes internal (heat) energy, warming it slightly.
The name given to the characteristic behaviour of substances which set their length perpendicular to a strong magnetic field instead of in line with it is
A.magnetization
B.paramagnetism
C.diamagnetism
D.demagnetization
E.ferromagnetism.
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Answer: C (diamagnetism)
Explanation
Diamagnetic materials are weakly repelled by a magnetic field, so a rod of such material turns to lie across the field. Paramagnetic and ferromagnetic rods line up along it.
What is the relative permitivity of a capacitor if its capacitance with a medium as dielectric is 16 farads and its capacitance with vacuum as dielectric is 2 farads?
A.−
B.½
C.2
D.8
E.32
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Answer: D (8)
Explanation
Relative permittivity = capacitance with dielectric ÷ capacitance with vacuum = 16/2 = 8.
A stand-by generator is connected to fifteen 40 W lamps and a musician's 600 W amplifying system. How much energy is used if the generator runs for 6 hours?
A.3.84 kWh
B.7.20 kWh
C.8.40 kWh
D.12.00 kWh
E.14.56 kWh.
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Answer: B (7.20 kWh)
Explanation
Total power = 15 × 40 + 600 = 1200 W = 1.2 kW. Energy = 1.2 × 6 = 7.2 kWh.
A tugboat is travelling from Asaba to Onitsha across the River Niger with a resultant velocity of 20 knots. If the river flows at 12 knots, the direction of motion of the boat relative to the direction of water flow is
A.36.87°
B.53.13°
C.90°
D.136.87°
E.143.13°.
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Answer: B (53.13°)
Explanation
The resultant (20 knots) is the hypotenuse, with the 12-knot river flow as the side next to the angle: cos θ = 12/20 = 0.6, so θ = 53.13°.
A milliammeter of resistance 5 Ω and full scale deflection of 50 mA is to be used to measure a potential difference of 50 V. The resistance of the multiplier should be
A.95 Ω
B.110 Ω
C.595 Ω
D.995 Ω
E.1005 Ω.
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Answer: D (995 Ω)
Explanation
At full scale, 50 V must drive 0.05 A through the meter plus the multiplier: 50 = 0.05 × (5 + R), so 5 + R = 1000 and R = 995 Ω.
The relative densities of zinc, brass, copper, gold and silver are respectively 7.1, 8.5, 8.9, 19.3, 10.5. A metal ornament which weighs 0.425 kg and can displace 50 × 10−6 m3 of water is made of
A.zinc
B.brass
C.copper
D.gold
E.silver.
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Answer: B (brass)
Explanation
Density = 0.425 ÷ (50 × 10−6) = 8500 kg m−3, a relative density of 8.5, which is brass.
In the above diagram MN is perpendicular to ON and MP. What is the difference between the moment about N of the force of 20 newtons applied along MP and its moment about O?
A.Zero
B.0.2 N m
C.0.4 N m
D.0.8 N m
E.0.6 N m
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Answer: A (Zero)
Explanation
MN = √(0.5² − 0.3²) = 0.4 m. The vertical 20 N force at M is 0.4 m (horizontally) from both N and O, so both moments are 20 × 0.4 = 8 N m and the difference is zero.
In the above diagram, a ray of light passes from glass into air. If the angle of incidence in glass is α and the angle of refraction in air is β, which of the following statements is true?
A.α = β
B.The refractive index of glass is sin θ/sin α
C.The ray suffers total internal reflection if β is greater than the critical angle
D.The ray will suffer total internal reflection if α is less than the critical angle
E.The refractive index of glass is sin α/sin β
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Answer: B (The refractive index of glass is sin θ/sin α)
Explanation
The refractive index of glass is sin(angle in air) ÷ sin(angle in glass) = sin β/sin α. Option E is upside down, and total internal reflection needs α greater than the critical angle.
In the above diagram a straight vertical wire is placed between two opposite magnetic poles which are separated horizontally by a short distance. If a current is passed down the wire, in which direction will the wire move?
A.Towards the observer
B.Away from the observer
C.Toward the North pole
D.Towards the South pole
E.Upwards
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Answer: A (Towards the observer)
Explanation
The field runs from N (left) to S (right) and the current flows downwards. Fleming's left-hand rule gives a force out of the page, towards the observer.
A calorimeter of thermal capacity 80 J contains 20 g of water at 25°C. Water at 100°C is added so that the final temperature of the set-up is 50°C. The amount of water added is (Heat capacity of water = 4.18 J/g/°C)
A.20 g
B.25 g
C.45 g
D.50 g
E.100 g.
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Answer: A (20 g)
Explanation
Heat lost by hot water = heat gained: m × 4.18 × 50 = 80 × 25 + 20 × 4.18 × 25 = 2000 + 2090. So 209m = 4090 and m ≈ 20 g.
A man stands one-third of the way between two walls and claps his hands. He hears two distinct echoes 1 s apart. If the speed of sound is 330 m s−1 the distance between the walls is
A.33 m
B.110 m
C.220 m
D.330 m
E.495 m
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Answer: E (495 m)
Explanation
If the walls are x apart, the echoes travel 2x/3 and 4x/3, a difference of 2x/3. Then 2x/3 = 330 × 1, so x = 495 m.
A cell has an open circuit voltage V1 and a closed circuit voltage V2 when a current I is flowing through it. Therefore, the internal resistance of the cell is
A.V2/I
B.V1/I
C.(V1 + V2)/I
D.(V1 − V2)/I
E.(V2 − V1)/I.
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Answer: D ((V1 − V2)/I)
Explanation
The open-circuit voltage is the e.m.f., V1. With current flowing, V2 = V1 − Ir, so the 'lost volts' V1 − V2 = Ir and r = (V1 − V2)/I.
The activity of a radioactive substance depends on
A.temperature and purity
B.temperature and age
C.purity and age
D.age, purity and temperature
E.none of the above.
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Answer: C (purity and age)
Explanation
Activity depends on how many radioactive nuclei are present, which depends on how pure the sample is and how much has already decayed (its age). Temperature has no effect on radioactive decay.
Naturally radioactive nuclei emit alpha particles, beta particles and gamma rays. X-rays come from electron transitions or X-ray tubes, not from the nucleus.