No questions found
(a) State two SI base quantities other than mass, length and time. [2]
(b) A beam is clamped at one end and an object X is attached to the other end of the beam, as shown in Fig. 1.1.
The object X is made to oscillate vertically.
The time period $T$ of the oscillations is given by
$$ T = K \sqrt{\frac{Ml^3}{E}} $$
where $M$ is the mass of X,
$l$ is the length between the clamp and X,
$E$ is the Young modulus of the material of the beam
and $K$ is a constant.
(i) 1. Show that the SI base units of the Young modulus are $\text{kg m}^{-1} \text{s}^{-2}$. [1]
2. Determine the SI base units of $K$. [2]
(ii) Data in SI units for the oscillations of X are shown in Fig. 1.2.
Calculate $E$ and its actual uncertainty. [4]
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The signal from a microwave detector is recorded on a cathode-ray oscilloscope (c.r.o.), as shown in Fig. 2.1.
The time-base setting on the c.r.o. is 50 ps cm^{-1}.
(a) Using Fig. 2.1, determine the wavelength of the microwaves. [4]
(b) The signal from a radio wave detector is recorded on the same c.r.o. The wavelength of the radio waves is 1.5 \times 10^{3} m.
Determine the time-base setting required to display the same number of oscillations on the c.r.o. as shown in Fig. 2.1. [2]
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600
(a) An object is moved from point P to point R either by a direct path or by the path P to Q to R, as shown in Fig. 3.1.
P and Q are on the same horizontal level. R is vertically above Q.
Explain whether the work done moving the object against the gravitational field is the same or different along paths PR and PQR. [2]
(b) A ball is thrown with an initial velocity $V$ at an angle $\theta$ to the horizontal, as shown in Fig. 3.2.
The variation with time $t$ of the height $h$ of the ball is shown in Fig. 3.3.
Air resistance is negligible.
(i) Use the time to reach maximum height to determine the vertical component $V_v$ of the velocity of the ball for time $t = 0$. [2]
(ii) The horizontal displacement of the ball at $t = 3.00 \text{s}$ is $25.5 \text{m}$. On Fig. 3.4, draw the variation with $t$ of the horizontal displacement $x$ of the ball. [1]
(iii) For the ball at maximum height, calculate the ratio [3]
$$ \frac{\text{potential energy of the ball}}{\text{kinetic energy of the ball}}. $$
(iv) In practice, air resistance is not negligible. State and explain the effect of air resistance on the time taken for the ball to reach maximum height. [2]
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Figure 1 shows a metal cylinder of height 4.5 cm and base area 24 cm2.
The density of the metal is 7900 kg m−3.
(a) Show that the mass of the cylinder is 0.85 kg.
(b) The cylinder is placed on a plank, as shown in figure 2.
The plank is at an angle of 40° to the horizontal. Calculate the pressure on the plank due to the cylinder. [3]
(c) The cylinder then slides down the plank with a constant acceleration of 3.8 m s−2.
A constant frictional force \( f \) acts on the cylinder.
Calculate the frictional force \( f \). [3]
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(a) A progressive wave transfers energy. A stationary wave does not transfer energy. State two other differences between progressive waves and stationary waves.
(b) A stationary wave is formed on a stretched string between two fixed points A and B. The variation of the displacement $y$ of particles of the string with distance $x$ along the string for the wave at time $t = 0$ is shown on Fig. 5.1.
The wave has a period of 20 ms and a wavelength of 1.2 m. The maximum amplitude of the particles of the string is 5.0 mm.
(i) On Fig. 5.1, draw a line to represent the position of the string at $t = 5.0$ ms. [2]
(ii) State the phase difference between the particles of the string at $x = 0.40$ m and at $x = 0.80$ m. [1]
(iii) State and explain the change in the kinetic energy of a particle at an antinode between $t = 0$ and $t = 5.0$ ms. A numerical value is not required.
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(a) Define electromotive force (e.m.f.) for a battery.
..............................................................................................................................
.............................................................................................................................. [1]
(b) A battery of e.m.f. 6.0V and internal resistance 0.50Ω is connected in series with two resistors X and Y, as shown in Fig. 6.1.
[Image_Fig_6.1]
The resistance of X is 4.0Ω and the resistance of Y is 12Ω. Calculate
(i) the current in the circuit,
current = ........................................................ A [2]
(ii) the terminal potential difference (p.d.) across the battery.
p.d. = ............................................................... V [1]
(c) A resistor Z is now connected in parallel with resistor Y in the circuit in (b). The new arrangement is shown in Fig. 6.2.
[Image_Fig_6.2]
Resistor Y is made from a wire of length $l$ and diameter $d$. Resistor Z is a wire made from the same material as Y. The length of the wire for Z is $l/2$ and the diameter is $d/2$.
(i) Calculate the resistance $R$ of the combination of resistors Y and Z.
$R = ............................................................... \Omega$ [3]
(ii) State and explain the effect on the terminal p.d. across the battery.
A numerical value is not required.
..............................................................................................................................
..............................................................................................................................
.............................................................................................................................. [2]
(d) For the circuits given in (b) and (c), show that the ratio
$$\frac{\text{power developed in the external circuit in Fig. 6.1}}{\text{power developed in the external circuit in Fig. 6.2}}$$
is approximately 0.8. [3]
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Two parallel, vertical metal plates in a vacuum are connected to a power supply and a switch, as shown in Fig. 7.1.
Fig. 7.1
A radioactive source emitting $\alpha$-particles is placed below the plates. The path of the $\alpha$-particles is shown on Fig. 7.1. The switch is closed producing a potential difference (p.d.) across the plates. This gives rise to a uniform electric field between the plates.
The separation of the plates is 12mm.
(a)
(i) On Fig. 7.1, draw the path of the $\alpha$-particles. [1]
(ii) Explain why the metal plates are placed in a vacuum.
....................................................................................................................................
.................................................................................................................................... [1]
(iii) Calculate the p.d. required to produce an electric field of $140 \, \text{MVm}^{-1}$.
p.d. = .............................. MV [2]
(b) The $\alpha$-particle source is replaced by a $\beta$-particle source. By reference to the properties of $\alpha$-radiation and $\beta$-radiation, suggest three possible differences in the deflection observed with $\beta$-particles.
1. ...................................................................................................................................
....................................................................................................................................
2. ...................................................................................................................................
....................................................................................................................................
3. ...................................................................................................................................
.................................................................................................................................... [3]
(c) Complete Fig. 7.2 to show the changes in the proton number $Z$ and the nucleon number $A$ of different radioactive nuclei when either an $\alpha$-particle or a $\beta$-particle is emitted.
[Table_1]
emitted particle | change in $Z$ | change in A
--------------------------------------------------------------
$\alpha$-particle |
$\beta$-particle |
Fig. 7.2 [1]
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