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(a) The diameter $d$ of a cylinder is measured as 0.0125 m $\pm$ 1.6%.
Calculate the absolute uncertainty in this measurement. [1]
(b) The cylinder in (a) stands on a horizontal surface. The pressure $p$ exerted on the surface by the cylinder is given by $$p = \frac{4W}{\pi d^2} .$$
The measured weight $W$ of the cylinder is 0.38 N $\pm$ 2.8%.
(i) Calculate the pressure $p$. [1]
(ii) Determine the absolute uncertainty in the value of $p$. [2]
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(a) State Newton's second law of motion. [1]
(b) A car of mass 850 kg tows a trailer in a straight line along a horizontal road, as shown in Fig. 2.1.
The car and the trailer are connected by a horizontal tow-bar.
The variation with time $t$ of the velocity $v$ of the car for a part of its journey is shown in Fig. 2.2.
(i) Calculate the distance travelled by the car from time \( t = 0 \) to \( t = 10 \) s. [2]
(ii) At time \( t = 10 \) s, the resistive force acting on the car due to air resistance and friction is 510 N. The tension in the tow-bar is 440 N.
For the car at time \( t = 10 \) s:
1. use Fig. 2.2 to calculate the acceleration [2]
2. use your answer to calculate the resultant force acting on the car [1]
3. show that a horizontal force of 1300 N is exerted on the car by its engine[1]
4. determine the useful output power of the engine. [2]
(c) A short time later, the car in (b) is travelling at a constant speed and the tension in the tow-bar is 480 N.
The tow-bar is a solid metal rod that obeys Hooke's law. Some data for the tow-bar are listed below.
Young modulus of metal = \( 2.2 \times 10^{11} \) Pa
original length of tow-bar = 0.48 m
cross-sectional area of tow-bar = \( 3.0 \times 10^{-4} \text{ m}^{2} \)
Determine the extension of the tow-bar. [3]
(d) The driver of the car in (b) sees a pedestrian standing directly ahead in the distance. The driver operates the horn of the car from time \( t = 15 \) s to \( t = 17 \) s. The frequency of the sound heard by the pedestrian is 480 Hz. The speed of the sound in the air is 340 m/s.
Use Fig. 2.2 to calculate the frequency of the sound emitted by the horn. [2]
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(a) State what is meant by the $\textit{centre of gravity}$ of a body. [1]
(b) A uniform square sign with sides of length 0.68 m is fixed at its corner points A and B to a wall. The sign is also supported by a wire CD, as shown in Fig. 3.1.
The sign has weight $W$ and centre of gravity at point E. The sign is held in a vertical plane with side BC horizontal. The wire is at an angle of 35° to side BC. The tension in the wire is 54 N.
The force exerted on the sign at B is only in the vertical direction.
(i) Calculate the vertical component of the tension in the wire. [1]
(ii) Explain why the force on the sign at B does not have a moment about point A. [1]
(iii) By taking moments about point A, show that the weight $W$ of the sign is 150 N. [2]
(iv) Calculate the total vertical force exerted by the wall on the sign at points A and B. [1]
(c) The sign in (b) is held together by nuts and bolts. One of the nuts falls vertically from rest through a distance of 4.8 m to the pavement below. The nut lands on the pavement with a speed of 9.2 m $s^{-1}$.
Determine, for the nut falling from the sign to the pavement, the ratio [4]
$$\frac{\text{change in gravitational potential energy}}{\text{final kinetic energy}}.$$
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(a) For a progressive water wave, state what is meant by:
(i) displacement [1]
(ii) amplitude. [1]
(b) Two coherent waves X and Y meet at a point and superpose. The phase difference between the waves at the point is 180°. Wave X has an amplitude of 1.2 cm and intensity I. Wave Y has an amplitude of 3.6 cm.
Calculate, in terms of I, the resultant intensity at the meeting point. [2]
(c) (i) Monochromatic light is incident on a diffraction grating. Describe the diffraction of the light waves as they pass through the grating. [2]
(ii) A parallel beam of light consists of two wavelengths 540 nm and 630 nm. The light is incident normally on a diffraction grating. Third-order diffraction maxima are produced for each of the two wavelengths. No higher orders are produced for either wavelength.
Determine the smallest possible line spacing $d$ of the diffraction grating. [3]
(iii) The beam of light in (c)(ii) is replaced by a beam of blue light incident on the same diffraction grating.
State and explain whether a third-order diffraction maximum is produced for this blue light. [2]
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(a) State Kirchhoff’s second law.
...........................................................................................................................
........................................................................................................................... [2]
(b) A battery of electromotive force (e.m.f.) 5.6 V and internal resistance $r$ is connected to two external resistors, as shown in Fig. 5.1.
The reading on the voltmeter is 4.8 V.
(i) Calculate:
1. the combined resistance of the two resistors connected in parallel
combined resistance = ..................................................... Ω [2]
2. the current in the battery.
current = ................................................................. A [2]
(ii) Show that the internal resistance $r$ is 2.5 Ω. [2]
(iii) Determine the ratio
$$\frac{\text{power dissipated by internal resistance } r}{\text{total power produced by battery}}.$$
ratio = ................................................................. [3]
(c) The battery in (b) is now connected to a battery of e.m.f. 7.2 V and internal resistance 3.5 Ω. The new circuit is shown in Fig. 5.2. Determine the current in the circuit.
current = ................................................................. A [2]
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(a) State what is meant by a field line (line of force) in an electric field. .................................................................................................................................................................. ..................................................................................................................................................................
(b) An electric field has two different regions X and Y. The field strength in X is less than that in Y. Describe a difference between the pattern of field lines (lines of force) in X and in Y. .................................................................................................................................................................. ..................................................................................................................................................................
(c) A particle P has a mass of 0.15 u and a charge of -1e, where e is the elementary charge.
(i) Particle P and an \( \alpha \)-particle are in the same uniform electric field. Calculate the ratio \[ \text{ratio} = \frac{\text{magnitude of acceleration of particle P}}{\text{magnitude of acceleration of } \alpha \text{-particle}}. \] ratio = ........................................................................... [3]
(ii) Particle P is a hadron composed of only two quarks. One of them is a down (d) quark.
By considering charge, determine a possible type (flavour) of the other quark. Explain your working. .................................................................................................................................................................. .................................................................................................................................................................. [3]
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