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(a) A unit may be stated with a prefix that represents a power-of-ten multiple or submultiple.
Complete Table 1.1 to show the name and symbol of each prefix and the corresponding power-of-ten multiple or submultiple. [2]
Table 1.1
(b) In the following list, underline all the units that are SI base units.
ampere coulomb metre newton [1]
(c) The potential difference $V$ between the two ends of a uniform metal wire is given by
$$V = \frac{4\rho LI}{\pi d^2}$$
where $d$ is the diameter of the wire,
$I$ is the current in the wire,
$L$ is the length of the wire,
and $\rho$ is the resistivity of the metal.
For a particular wire, the percentage uncertainties in the values of some of the above quantities are listed in Table 1.2.
Table 1.2
The quantities listed in Table 1.2 have values that are used to calculate $\rho$ as $4.1 \times 10^{-7} \Omega \text{ m}$.
For this value of $\rho$, calculate:
(i) the percentage uncertainty [2]
(ii) the absolute uncertainty. [1]
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508
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A charged oil drop is in a vacuum between two horizontal metal plates. A uniform electric field is produced between the plates by applying a potential difference of 1340 V across them, as shown in Fig. 2.1.
The separation of the plates is $1.4 \times 10^{-2} \text{ m}$.
The oil drop of weight $4.6 \times 10^{-14} \text{ N}$ remains stationary at a point mid-way between the plates.
(a) (i) Calculate the magnitude of the electric field strength.
electric field strength = ............................................... $\text{NC}^{-1}$ [2]
(ii) Determine the magnitude and the sign of the charge on the oil drop.
magnitude of charge = .................................................. $\text{C}$
sign of charge ................................................................ [3]
(b) The electric potentials of the plates are instantaneously reversed so that the top plate is at a potential of 0 V and the bottom plate is at a potential of +1340 V. This change causes the oil drop to start moving downwards.
(i) Compare the new pattern of the electric field lines between the plates with the original pattern.
.................................................................................................................. [2]
(ii) Determine the magnitude of the resultant force acting on the oil drop.
resultant force = ....................................................... $\text{N}$ [1]
(iii) Show that the magnitude of the acceleration of the oil drop is $20 \text{ ms}^{-2}$.
.................................................................................................................. [2]
(iv) Assume that the radius of the oil drop is negligible.
Use the information in (b)(iii) to calculate the time taken for the oil drop to move to the bottom metal plate from its initial position mid-way between the plates.
time = ............................................................. $\text{s}$ [2]
(c) The oil drop in (b) starts to move at time $t = 0$. The distance of the oil drop from the bottom plate is $x$.
On Fig. 2.2, sketch the variation with time $t$ of distance $x$ for the movement of the drop from its initial position until it hits the surface of the bottom plate. Numerical values of $t$ are not required.
[2]
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511
(a) Define power. [1]
(b) A car of mass 1700 kg moves in a straight line along a slope that is at an angle $\theta$ to the horizontal, as shown in Fig. 3.1.
The car moves at constant velocity for a distance of 25 m from point A to point B. Air resistance and friction provide a total resistive force of 440 N that opposes the motion of the car.
For the movement of the car from A to B:
(i) state the change in the kinetic energy [1]
(ii) calculate the work done against the total resistive force. [1]
(c) The movement of the car in (b) from A to B causes its gravitational potential energy to increase by $4.8 \times 10^4$ J.
Calculate.
(i) the increase in vertical height $h$ of the car for its movement from A to B [2]
(ii) angle $\theta$. [1]
(d) The engine of the car in (b) produces an output power of $1.7 \times 10^4$ W to move the car along the slope.
Calculate the time taken for the car to move from A to B. [2]
547
521
581
A child sits on the ground next to a remote-controlled toy car. At time $t = 0$, the car begins to move in a straight line directly away from the child. The variation with time $t$ of the velocity of the car along this line is shown in Fig. 4.1.
The car’s horn continually emits sound of frequency 925 Hz between time $t = 0$ and time $t = 6.0$ s.
The speed of the sound in the air is 338 m s$^{-1}$.
(a) Describe qualitatively the variation, if any, in the frequency of the sound heard, by the child, that was emitted from the car horn:
(i) from time $t = 0$ to time $t = 2.0$ s [1]
(ii) from time $t = 4.0$ s to time $t = 6.0$ s. [1]
(b) Determine the frequency, to three significant figures, of the sound heard, by the child, that was emitted from the car horn at time $t = 3.0$ s. [2]
(c) Determine the time taken for the sound emitted at time $t = 4.0$ s to travel to the child. [2]
525
504
562
A tube is initially fully submerged in water. The axis of the tube is kept vertical as the tube is slowly raised out of the water, as shown in Fig. 5.1.
A loudspeaker producing sound of frequency 530 Hz is positioned at the open top end of the tube as it is raised. The water surface inside the tube is always level with the water surface outside the tube. The speed of the sound in the air column in the tube is 340 m s⁻¹.
(a) Describe a simple way that a student, without requiring any additional equipment, can detect when a stationary wave is formed in the air column as the tube is being raised. [1]
(b) Determine the height of the top end of the tube above the surface of the water when a stationary wave is first produced in the tube. Assume that an antinode is formed level with the top of the tube. [3]
(c) Determine the distance moved by the tube between the positions at which the first and second stationary waves are formed. [1]
500
542
581
A cell of electromotive force (e.m.f.) 0.48 V is connected to a metal wire X, as shown in Fig. 6.1.
The cell has internal resistance. The current in the cell is 0.80 A.
Wire X has length 3.0 m, cross-sectional area $1.3 \times 10^{-7} \text{ m}^2$ and resistance 0.40 $\Omega$.
(a) Calculate the charge passing through the cell in a time of 7.5 minutes.
charge = ................................................ C [2]
(b) Calculate the percentage efficiency with which the cell supplies power to wire X.
efficiency = ..................................................... % [3]
(c) There are $3.2 \times 10^{22}$ free (conduction) electrons contained in the volume of wire X.
For wire X, calculate:
(i) the number density $n$ of the free electrons
$n = ..................................................... \text{ m}^{-3}$ [1]
(ii) the average drift speed of the free electrons.
average drift speed = ..................................................... $\text{ m s}^{-1}$ [2]
(d) A wire Y has the same cross-sectional area as wire X and is made of the same metal. Wire Y is longer than wire X.
Wire X in the circuit is now replaced by wire Y. Assume that wire Y has the same temperature as wire X.
State and explain whether the average drift speed of the free electrons in wire Y is greater than, the same as, or less than that in wire X.
....................................................................................................................................................
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....................................................................................................................................................
....................................................................................................................................................
....................................................................................................................................................
[3]
559
533
591
A stationary nucleus P of mass 243 u decays by emitting an $\alpha$-particle of mass 4 u to form a different nucleus Q, as illustrated in Fig. 7.1.
The initial speed of the $\alpha$-particle is $1.6 \times 10^7 \text{ m s}^{-1}$.
(a) Use the principle of conservation of momentum to explain why the initial velocities of nucleus Q and the $\alpha$-particle must be in opposite directions.
........................................................................................................................................................................
........................................................................................................................................................................
........................................................................................................................................................................
........................................................................................................................................................................ [2]
(b) Determine the initial speed $v$ of nucleus Q.
$v =$ ............................................................. $\text{ms}^{-1}$ [2]
(c) Calculate the initial kinetic energy, in MeV, of the $\alpha$-particle.
kinetic energy = ......................................................... MeV [3]
(d) A graph of number of neutrons $N$ against proton number $Z$ is shown in Fig. 7.2.
The graph shows a cross that represents nucleus P.
A nucleus R has a nucleon number of 242 and is an isotope of nucleus P.
Nucleus R decays by emitting a $\beta^-$ particle to form a different nucleus S.
(i) On Fig. 7.2, draw a cross to represent:
1. nucleus R (label this cross R)
2. nucleus S (label this cross S). [2]
(ii) State the name of the other lepton, in addition to the $\beta^-$ particle, that is emitted during the decay of nucleus R.
................................................................................................................ [1]
519
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529
