47 questions. Try each one, then open the answer to check yourself and read the explanation.
A hand bag containing some load weighing 162 N is carried by two students each holding the handle of the bag next to him. If each handle is pulled 60° to the vertical, find the force on each student's arm.
Answer: B (162 N)
Each pull T has a vertical part T cos 60° = T/2. The two together hold up the bag: 2 × T/2 = 162, so T = 162 N.
I. The frictional force is independent of the area of the surfaces in contact.
II. The frictional force depends on the nature of the surfaces in contact.
III. The frictional force depends on the speed of sliding.
IV. The frictional force is directly proportional to the normal reaction.
Which combination of the above is true of sliding friction?
Answer: A (I, II and IV)
The laws of sliding friction: it does not depend on contact area or (roughly) on speed, it depends on the surfaces, and it is proportional to the normal reaction. So I, II and IV.
When a ship sails from salt water into fresh water, the fraction of its volume above the water surface will
Answer: C (decrease)
Fresh water is less dense, so the ship must sink deeper to displace its own weight; less of it stays above the surface.
A simple pendulum has a period of 17.0 s. When the length is shortened by 1.5 m, its period is 8.5 s. Calculate the original length of the pendulum.
Answer: B (2.0 m)
T ∝ √L, so (17/8.5)2 = L/(L − 1.5), i.e. 4 = L/(L − 1.5). Then 4L − 6 = L and L = 2.0 m.
At a fixed point below a liquid surface, the pressure downward is P1 and the pressure upward is P2. It can be deduced that
Answer: A (P1 = P2)
Pressure at a point in a liquid acts equally in all directions, so the downward and upward pressures at the same point are equal.
I. Its velocity is constant
II. No work is done on the body.
III. It has constant acceleration directed away from the centre.
IV. The centripetal force is directed towards the centre.
Which combination of the above is true of a body moving with constant speed in a circular track?
Answer: D (II and IV)
The direction keeps changing, so velocity is not constant (I false) and acceleration is towards the centre (III false). The force is towards the centre and at right angles to the motion, so it does no work (II, IV true).
The velocity v of a particle in a time t is given by the equation v = 10 + 2t2. Find the instantaneous acceleration after 5 seconds.
Answer: C (20 m s−2)
a = dv/dt = 4t. At t = 5 s, a = 20 m s−2.
If the force and the velocity on a system are each reduced simultaneously by half, the power of the system is
Answer: C (reduced to a quarter)
Power = force × velocity, so halving both gives ½ × ½ = ¼ of the original power.
The velocity ratio of a machine is 5 and its efficiency is 75%. What effort would be needed to lift a load of 150 N with the machine?
Answer: B (40 N)
MA = efficiency × VR = 0.75 × 5 = 3.75. Effort = load ÷ MA = 150/3.75 = 40 N.
A rope is being used to pull a mass of 10 kg vertically upward. Determine the tension in the rope if, starting from rest, the mass acquires a velocity of 4 m s−1 in 8 s. [g = 10 m s−2]
Answer: A (105 N)
a = 4/8 = 0.5 m s−2 upwards. T − mg = ma, so T = 10 × 10 + 10 × 0.5 = 105 N.
I. Coherence II. Same frequency III. Same wavelength IV. Same intensity
Which of the conditions above are necessary to produce interference fringes?
Answer: A (I, II and III)
Interference needs coherent sources, which have the same frequency and wavelength; equal intensity is not required.
An engineer intends to deviate a light ray from its path by 120° through reflection from a plane mirror. Calculate the angle of incidence.
Answer: B (30°)
Deviation by a plane mirror = 180° − 2i. So 180 − 2i = 120 and i = 30°.
Dry bulb: Day 1 30 °C, Day 2 29 °C, Day 3 25 °C
Wet bulb: Day 1 22 °C, Day 2 22 °C, Day 3 21 °C
The readings above are for three consecutive days from a wet and dry bulb hygrometer. It can be concluded that the relative humidity for the three days
Answer: A (increased steadily)
The difference between dry and wet readings fell from 8 °C to 7 °C to 4 °C. A smaller difference means less evaporation, so the air was getting more humid each day.
Total internal reflection occurs when light moves from
Answer: C (a dense medium to a less dense medium)
Total internal reflection can only happen when light goes from an optically denser medium towards a less dense one, at more than the critical angle.
One end of a long wire is fixed while a vibrator is attached to the other end. When the vibrator is energized, the types of waves generated in the wire are
Answer: A (stationary and transverse)
The vibrator shakes the wire sideways, making transverse waves; these reflect at the fixed end and combine with the incoming waves to form stationary waves.
A sonometer wire is vibrating at frequency fo. If the tension in the wire is doubled while the length and the mass per unit length are kept constant, the new frequency of vibration is
Answer: D (fo√2)
f ∝ √T, so doubling the tension multiplies the frequency by √2: fo√2.
A boy observes a piece of stone at the bottom of a river 6.0 m deep. If he looks from the surface of the river, what is the apparent distance of the stone from him? [Refractive index of water = 4/3]
Answer: A (4.5 m)
Apparent depth = real depth ÷ refractive index = 6.0 ÷ (4/3) = 4.5 m.
A metal of mass 0.5 kg is heated to 100 °C and then transferred to a well-lagged calorimeter of heat capacity 80 J K−1 containing water of heat capacity 420 J K−1 at 15 °C. If the final steady temperature of the mixture is 25 °C, find the specific heat capacity of the metal.
Answer: B (133 J kg−1 K−1)
Heat lost by metal = heat gained by calorimeter and water: 0.5 × c × 75 = (80 + 420) × 10 = 5000. So c = 5000/37.5 ≈ 133 J kg−1 K−1.
The diagram above shows a maximum and minimum thermometer divided into three portions P, Q and R. Which of the following is true about the respective contents of P, Q and R?
Answer: A (Alcohol, mercury and alcohol)
In Six's maximum and minimum thermometer the bulb P is full of alcohol, the U-bend Q holds a thread of mercury, and above the mercury on the other side R is alcohol again.
The main reason for making the cover of a vacuum flask airtight is to prevent heat loss by
Answer: D (convection)
The airtight stopper stops warm air (and vapour) from circulating out of the flask, so it cuts heat loss by convection; radiation is reduced by the silvered walls, not the cover.
A travelling wave moving from left to right has an amplitude of 0.15 m, a frequency of 550 Hz and a wavelength of 0.01 m. The equation describing the wave is
Answer: A (y = 0.15 sin 200π (x − 5.5t))
k = 2π/λ = 2π/0.01 = 200π and ω = 2πf = 1100π = 200π × 5.5. So y = 0.15 sin(200πx − 1100πt) = 0.15 sin 200π(x − 5.5t).
A transverse wave is applied to a string whose mass per unit length is 3 × 10−2 kg m−1. If the string is under a tension of 12 N, the speed of propagation of the wave is
Answer: C (20 m s−1)
v = √(T/μ) = √(12/0.03) = √400 = 20 m s−1.
A quantity of water at 0 °C is heated to about 30 °C. At each degree rise in temperature, its density will
Answer: B (rise then fall)
Water is densest at 4 °C, so its density rises from 0 °C to 4 °C and then falls as it is heated further.
A thin wire with heavy weights attached to boths ends is hung over a block of ice resting on two supports. If the wire cuts through the ice block while the block remains solid behind the wire, the process is called.
Answer: D (regelation.)
Pressure under the wire lowers the melting point so the ice melts there; the water refreezes above the wire once the pressure is removed. This is regelation.
A cell of internal resistance 0.01 Ω can be measured accurately using the
Answer: B (potentiometer)
A potentiometer draws no current at balance, so it can compare e.m.f. and terminal p.d. accurately enough to find a very small internal resistance.
An electron of charge 1.6 × 10−19 C and mass 9.1 × 10−31 kg is accelerated between two metal plates with velocity of 4 × 107 m s−1, the potential difference between the plates is
Answer: D (4.55 × 103 V)
eV = ½mv2, so V = 9.1 × 10−31 × (4 × 107)2 ÷ (2 × 1.6 × 10−19) = 4.55 × 103 V.
In the diagram above, a beam of white light travels from a rare to a dense medium. What colours of light do the rays a, b, and c respectively represent?
Answer: A (Blue, yellow and red)
Blue light slows down most in the denser medium, so it bends most towards the normal (ray a); red bends least (ray c). Yellow lies between them.
The diagram above shows two capacitors P and Q of capacitances 5 μF and 10 μF. Find the charges stored in P and Q respectively.
Answer: B (100 μC and 200 μC)
P and Q are in parallel across 20 V, so Q = CV: 5 μF × 20 V = 100 μC and 10 μF × 20 V = 200 μC.
What optical instrument can best be constructed with converging lenses of focal lengths 50 cm and 5 cm?
Answer: C (Astronomical telescope)
An astronomical telescope uses two converging lenses: a long-focus objective (50 cm) and a short-focus eyepiece (5 cm). A Galilean telescope needs a diverging eyepiece.
If a charged ion goes through combined electric and magnetic fields, the resultant emergent velocity of the ion is
Answer: A (E/B)
The ion passes straight through when the electric and magnetic forces balance: qE = qvB, so v = E/B.
In the diagram above, the values of V1 and V2 are respectively
Answer: D (1 V and ⅔ V)
Total resistance = 3 + 2 + 1 = 6 Ω, so I = 2/6 = ⅓ A. V1 = ⅓ × 3 = 1 V and V2 = ⅓ × 2 = ⅔ V.
A projection lantern is used to give the image of a slide on a screen. If the image is 24 times as large as the slide and the screen is 72.0 m from the projecting lens, what is the position of the slide from the lens?
Answer: C (3.0 m)
Magnification = v/u, so 24 = 72/u and u = 3.0 m.
A radio is operated by eight cells each of e.m.f. 2.0 V connected in series. If two of the cells are wrongly connected, the net e.m.f. of the radio is
Answer: D (8 V)
Six cells push one way (12 V) and the two reversed cells push the other way (4 V), so the net e.m.f. is 12 − 4 = 8 V.
A 2 H inductor has negligible resistance and is connected to a 50/π Hz a.c supply. The reactance of the inductor is
Answer: A (200 Ω)
XL = 2πfL = 2π × (50/π) × 2 = 200 Ω.
If the fraction of the atoms of a radioactive material left after 120 years is 1/64, what is the half-life of the material?
Answer: C (20 years)
1/64 = (½)6, so 6 half-lives took 120 years. Half-life = 120/6 = 20 years.
A certain radioactive source emits radiations that were found to be deflected by both magnetic and electric fields. The radiations are
Answer: B (beta rays)
Only charged particles are deflected by electric and magnetic fields. Beta rays are electrons; X-rays, gamma rays and UV are uncharged electromagnetic waves.
In a pure semiconductor, the number of electrons in the conduction band is
Answer: A (equal to the number of holes in the valence band)
In a pure (intrinsic) semiconductor each electron that jumps to the conduction band leaves one hole behind, so the numbers are equal.
A cell of internal resistance 1 Ω supplies current to an external resistor of 3 Ω. The efficiency of the cell is
Answer: A (75%)
Efficiency = useful power/total power = R/(R + r) = 3/(3 + 1) = 75%.
Light of energy 5 eV falls on a metal of work function 3 eV and electrons are liberated. The stopping potential is
Answer: C (2.0 V)
Maximum KE of the electrons = 5 − 3 = 2 eV, so a stopping potential of 2.0 V is needed.
In a thermonuclear reaction, the total initial mass is 5.02 × 10−27 kg and the total final mass is 5.01 × 10−27 kg. The energy released in the process is
Answer: D (9.0 × 10−13 J)
Mass lost = 0.01 × 10−27 = 10−29 kg. E = mc2 = 10−29 × (3 × 108)2 = 9.0 × 10−13 J.
The magnetic flux in a coil having 200 turns changes at the time rate of 0.08 Wb s−1. The induced e.m.f. in the coil is
Answer: B (16.0 V)
E = N × rate of change of flux = 200 × 0.08 = 16.0 V.
If the frequency of an emitted x-rays is 1.6 × 1016 Hz, the accelerating potential is [e = 1.6 × 10−19 C, h = 6.63 × 10−34 J s]
Answer: B (66.3 V)
eV = hf, so V = 6.63 × 10−34 × 1.6 × 1016 ÷ 1.6 × 10−19 = 66.3 V.
The correct position for a fuse in the diagram above is
Answer: C (P)
A fuse always goes in the live wire, so that when it blows the device is cut off from the high voltage. P is on the live wire.
In the a.c circuit above, the current value is
Answer: B (4.00 A)
Impedance Z = √(302 + 402) = 50 Ω, so I = V/Z = 200/50 = 4.00 A.
A gas would serve as an electrical conductor under
Answer: B (reduced pressure and high current)
Gases conduct (as in a discharge tube) at low pressure with a high voltage driving a current through them; the other conditions do not ionise the gas.
An electric generator with a power output of 3.0 kW at a voltage of 1.5 kV distributes power along cables of total resistance 20.0 Ω. The power loss in the cable is
Answer: D (80.0 W)
I = P/V = 3000/1500 = 2 A. Power lost = I2R = 22 × 20 = 80.0 W.
A conductor of length 2 m carries a current of 0.8 A while kept in a magnetic field of magnetic flux density 0.5 T. The maximum force acting on it is
Answer: C (0.8 N)
F = BIL sin θ is largest when θ = 90°: F = 0.5 × 0.8 × 2 = 0.8 N.