46 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following is a fundamental unit?
Answer: D (Second)
The second is an SI base unit. The newton, watt and joule are derived from base units.
Two horizontal forces, 10 N and 8 N and another force F1 inclined at 30° to the vertical acting as shown in the diagram above, keep the body P in equilibrium. The weight of the body is
Answer: D (2√3 N)
Horizontally, F1 sin 30° must make up the 2 N difference, so F1 = 4 N. Vertically the weight equals F1 cos 30° = 4 × (√3/2) = 2√3 N.
A car moving with a speed of 90 km h−1 was brought uniformly to rest by the application of the brakes in 10 s. How far did the car travel after the brakes were applied?
Answer: A (125 m)
90 km h−1 = 25 m s−1. Average speed while stopping uniformly = 12.5 m s−1, so the distance is 12.5 × 10 = 125 m.
A particle of mass M which is at rest splits up into two. If the mass and velocity of one of the particles are m and v respectively, calculate the velocity of the second particle.
Answer: D (mv/(M − m))
Total momentum stays zero, so the other piece, of mass M − m, has momentum mv the other way: V = mv/(M − m).
Which of the following statements are correct about an object in equilibrium under parallel forces? I. The total clockwise moments of the forces about any point equals the total anticlockwise moments about the same point. II. The total forces in one direction equals the total forces in the opposite direction III. The resolved components along the x-axis equals the resolved components along the y-axis.
Answer: A (I and II only)
For equilibrium the moments balance about any point and the forces in opposite directions balance. There is no rule that x-components must equal y-components.
A force of 5 N acts at a point Y on a rod XYZ as shown in the diagram above. If XY is 2 m, what is the moment of the force about point X?
Answer: A (0 N m)
The force acts along the rod itself, so its line of action passes through X. The perpendicular distance is zero and so is the moment.
To keep a vehicle moving at a constant speed v, requires power P, from the engine. The force provided by the engine is
Answer: A (P/v)
Power = force × velocity, so F = P/v.
A stone of mass m kg is held h meters above the floor for 50 s. The work done in joules over this period is
Answer: D (0)
Work needs movement in the direction of the force. The stone does not move, so no work is done.
A body of mass 10 kg rests on a rough inclined plane whose angle of tilt θ is variable. θ is gradually increased until the body starts to slide down the plane at 30°. The coefficient of limiting friction between the body and the plane is
Answer: C (0.58)
When the body just slides, μ = tan θ = tan 30° ≈ 0.58.
An inclined plane which makes an angle of 30° with the horizontal has a velocity ratio of
Answer: A (2)
VR = 1/sin θ = 1/sin 30° = 2.
What is the length of the liquid column in a barometer tube that would support an atmospheric pressure of 102000 N m−2 if the density of the liquid is 2600 kg m−3? [g = 10 m s−2]
Answer: C (3.92 m)
p = hρg, so h = 102 000/(2600 × 10) ≈ 3.92 m.
40 m3 of liquid P is mixed with 60 m3 of another liquid Q. If the density of P and Q are 1.00 kg m−3 and 1.6 kg m−3 respectively, what is the density of the mixture?
Answer: D (1.36 kg m−3.)
Total mass = 40 × 1.00 + 60 × 1.6 = 136 kg in 100 m3, so the density is 1.36 kg m−3.
The resistances of a platinum wire at the ice and steam points are 0.75 ohm and 1.05 ohm respectively. Determine the temperature at which the resistance of the wire is 0.90 ohm.
Answer: B (50.0°C)
θ = (0.90 − 0.75)/(1.05 − 0.75) × 100 = 0.15/0.30 × 100 = 50°C.
A bar of initial length l0 is heated through a temperature change Δt to a new length l. The linear expansivity, α, of the bar is
Answer: B ((l − l0)/(l0Δt))
Linear expansivity = increase in length ÷ (original length × temperature change) = (l − l0)/(l0Δt).
The pressure of a gas when cooled at constant volume will decrease because the molecules
Answer: A (collide less frequently with the walls of the container)
Cooling slows the molecules, so they hit the walls less often (and less hard), lowering the pressure.
1 kg of copper is transferred quickly from boiling water to a block of ice. Calculate the mass of ice melted, neglecting heat loss. [Specific heat capacity of copper − 400 J kg−1 K−1 and latent heat of fusion of ice − 333 × 103 J kg−1].
Answer: C (120 g)
Heat given out by copper cooling from 100°C to 0°C = 1 × 400 × 100 = 40 000 J. Ice melted = 40 000/333 000 ≈ 0.12 kg = 120 g.
Which of the following conditions will make water boil at a temperature of 100°C when the atmospheric pressure is 750 mm Hg?
Answer: A (Increase the external pressure)
Water boils at 100°C only at standard pressure, 760 mm Hg. At 750 mm Hg it boils below 100°C, so the pressure on it must be increased.
Which of the following statements are correct? I. Land and sea breezes are natural convection currents. II. Convection may occur in liquids or gases but not in solids. III. The vacuum in a thermos flask prevents heat loss due to convection only.
Answer: A (I and II only)
Breezes are convection currents, and convection needs a fluid. The vacuum stops conduction as well as convection, so III is wrong.
A light wave of frequency 5 × 1014 Hz moves through water which has a refractive index of 4/3. Calculate the wavelength in water if the velocity of light in air is 3 × 108 m s−1.
Answer: A (4.5 × 10−7 m)
Speed in water = 3 × 108 ÷ (4/3) = 2.25 × 108 m s−1. λ = v/f = 2.25 × 108/5 × 1014 = 4.5 × 10−7 m.
A wave disturbance travelling in air enters a medium in which its velocity is less than that in air. Which of the following statements is true about the wave in the medium?
Answer: C (The frequency of the wave is unaltered while the wavelength is decreased.)
The frequency is fixed by the source. With a lower speed, λ = v/f becomes shorter.
Shadows and eclipses result from the
Answer: B (rectilinear propagation of light)
Shadows and eclipses form because light travels in straight lines and cannot bend round opaque objects.
An object which is 3 cm high is placed vertically 10 cm in front of a concave mirror. If this object produces an image 40 cm from the mirror, the height of the image is
Answer: D (12.00 cm)
Magnification = v/u = 40/10 = 4, so the image is 4 × 3 = 12 cm high.
A boy looks at the image of an object in a plane mirror. He observes two images, a main bright one and the other faint. The observed images result from
Answer: D (reflection and refraction)
A glass mirror has two reflecting surfaces. The faint image comes from the front glass surface; the bright one from the silvered back, which the light reaches only after being refracted into the glass.
Which of the diagrams below correctly illustrates the path of a ray of light through a glass prism?
Answer: C (C)
A ray passing through a prism is bent towards the base at both faces. Only the top-right diagram (C) shows the ray bending towards the base as it enters and again as it leaves.
What must be the distance between an object and a converging lens of focal length 20 cm to produce an erect image two times the object height?
Answer: C (10 cm)
An erect, magnified image is virtual, with v = −2u. 1/u − 1/(2u) = 1/20 gives 1/(2u) = 1/20, so u = 10 cm.
For a short sighted person, light rays from a point on a very distant object is focused
Answer: A (in front of the retina)
A short-sighted eye is too strong (or too long), so parallel rays from far away meet in front of the retina.
When light is incident on an object which is magenta in colour, which of the following colours would be absorbed?
Answer: B (Green only)
Magenta is red + blue, so a magenta object reflects red and blue and absorbs green.
In a resonance tube experiment, the effective length of the air column for the first resonance is 20 cm when set into vibration by a tuning fork of frequency 480 Hz. Neglecting end effect, the velocity of sound in air is
Answer: D (384 m s−1)
First resonance: L = λ/4, so λ = 80 cm. v = fλ = 480 × 0.8 = 384 m s−1.
An organ pipe closed at one end is 80 cm long. Determine the frequency of the fundamental note assuming that the speed of sound in air is 340 m s−1.
Answer: A (106 Hz)
For a closed pipe λ = 4L = 3.2 m, so f = 340/3.2 ≈ 106 Hz.
A sonometer wire of length 100 cm under a tension of 10 N, has a frequency of 250 Hz. Keeping the length of the wire constant, the tension is adjusted to produce a new frequency of 350 Hz. The new tension is
Answer: D (19.6 N)
f ∝ √T, so T2 = 10 × (350/250)² = 10 × 1.96 = 19.6 N.
One of the properties of the earth's magnetic field is that the
Answer: C (earth's magnetic flux is entirely horizontal at a place where the magnetic dip is zero)
Dip is the angle the field makes with the horizontal, so where the dip is zero (the magnetic equator) the field is entirely horizontal.
Which of the following statements are true of an insulated charged body carrying a positive charge? I. It contains excess positive charges II. It creates an electric field III. It possesses potential energy IV. It carries electric current
Answer: C (I, II and III only)
A positively charged body has more positive than negative charge, sets up an electric field and has electrical potential energy. Being insulated, its charge is at rest, so no current flows.
Which of the following is a vector?
Answer: B (Electric field)
An electric field has both strength and direction. Charge, potential difference and capacitance are scalars.
Three cells each of e.m.f. 1.5 V and an internal resistance of 1.0 Ω are connected in parallel across a load resistance of 2.67 Ω. Calculate the current in the load?
Answer: C (0.50 A)
Identical cells in parallel give e.m.f. 1.5 V and internal resistance 1/3 Ω. I = 1.5/(2.67 + 0.33) = 0.5 A.
When a known standard resistor of 2.0 Ω is connected to the 0.0 cm end of a meter bridge, the balance point is found to be at 55.0 cm. What is the value of the unknown resistor?
Answer: B (1.64 Ω)
At balance R1/R2 = l1/l2: 2/R = 55/45, so R = 2 × 45/55 ≈ 1.64 Ω.
The total energy required to send a unit positive charge round a complete electrical circuit is the
Answer: C (electromotive force)
The e.m.f. of a source is defined as the energy it gives to each coulomb of charge driven round the whole circuit (including inside the source). Potential difference refers to only part of the circuit.
Which of the following graphs of current against voltage illustrates Ohm's law?
Answer: A (A)
Ohm's law means I is directly proportional to V: a straight line through the origin, as in A.
Which of the following is an essential physical property of the wires used for making fuses?
Answer: D (Low melting point)
A fuse wire must melt quickly when too much current heats it, so it needs a low melting point.
Electrical power is transmitted at a high voltage rather than low voltage because the amount of energy loss is reduced due to
Answer: A (heat dissipation)
At high voltage the current is small, so far less energy is lost as I²R heat in the cables.
A lamp is rated 240 V, 60 W. The resistance of the filament is
Answer: A (960 Ω)
R = V²/P = 240²/60 = 960 Ω.
A 0 − 10 mA galvanometer with a coil resistance of 30 Ω can be converted to a 0 − 10 A ammeter by using
Answer: B (0.03 Ω shunt resistor)
The shunt carries 10 − 0.01 = 9.99 A at the same p.d. as the meter: 9.99R = 0.01 × 30, so R ≈ 0.03 Ω, connected in parallel.
The number of neutrons contained in the nucleus of 23892U is
Answer: B (146)
Neutrons = mass number − atomic number = 238 − 92 = 146.
What precaution should a manufacturer take to ensure that energy loss in a transformer is minimized?
Answer: B (The core should be made of thin sheets of metal)
A core made of thin insulated (laminated) sheets cuts down eddy currents and the energy they waste.
A substance has a half life of 3 min. After 6 min, the count rate was observed to be 400. What was its count rate at zero time?
Answer: C (1600)
6 min is two half-lives, so the count rate has fallen to a quarter: original = 400 × 4 = 1600.
Which of the following graphs represents a voltage current characteristic curve for a diode?
Answer: B (B)
A diode passes almost no current until the forward voltage is large enough, then the current rises steeply: a curve like B.
The photocell works on the principle of the
Answer: B (emission of electrons by incident radiation)
In a photocell, light falling on a metal surface knocks out electrons (the photoelectric effect), which form a current.