No questions found
(a) Define density.
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..............................................................................................................................................................................................[1]
(b) The mass $m$ of a metal sphere is given by the expression
$m = \frac{\pi d^3 \rho}{6}$
where $\rho$ is the density of the metal and $d$ is the diameter of the sphere.
Data for the density and the mass are given in Fig. 1.1.
[Table_1]
Fig. 1.1
(i) Calculate the diameter $d$.
$d =$ ................................................... m [1]
(ii) Use your answer in (i) and the data in Fig. 1.1 to determine the value of $d$, with its absolute uncertainty, to an appropriate number of significant figures.
$d =$ ............................ $\pm$ ............................ m [3]
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(a) Define electric field strength.
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...............................................................................................................................[1]
(b) A potential difference of 2.5 kV is applied across a pair of horizontal metal plates in a vacuum, as shown in Fig. 2.1.
Each plate has a length of 5.9 cm. The separation of the plates is 4.0 cm. The arrangement produces a uniform electric field between the plates. Assume the field does not extend beyond the edges of the plates.
An electron enters the field at point A with horizontal velocity $3.7 \times 10^7 \mathrm{ms}^{-1}$ along a line mid-way between the plates. The electron leaves the field at point B.
(i) Calculate the time taken for the electron to move from A to B.
time taken = ................................................................. s [1]
(ii) Calculate the magnitude of the electric field strength.
field strength = ....................................................... $\mathrm{NC}^{-1}$ [2]
(iii) Show that the acceleration of the electron in the field is $1.1 \times 10^{16} \mathrm{ms}^{-2}$.
(iv) Use the acceleration given in (iii) and your answer in (i) to determine the vertical distance $y$ between point B and the upper plate.
$y = .................................................................$ cm [3]
(v) Explain why the calculation in (iv) does not need to include the gravitational effects on the electron.
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...............................................................................................................................[1]
(vi) The electron enters the field at time $t = 0$.
On Fig. 2.2, sketch graphs to show the variation with time $t$ of
1. the horizontal component $v_X$ of the velocity of the electron,
2. the vertical component $v_Y$ of the velocity of the electron.
Numerical values are not required.
[2]
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(a) State what is meant by the frequency of a progressive wave. [2]
(b) A cathode-ray oscilloscope (c.r.o.) is used to determine the frequency of the sound emitted by a loudspeaker. The trace produced on the screen of the c.r.o. is shown in Fig. 4.1.
The time-base setting of the c.r.o. is 250$\mu$s cm$^{-1}$.
Show that the frequency of the sound wave is 1600 Hz. [2]
(c) The loudspeaker in (b) emits the sound in all directions. A person attaches the loudspeaker to a string and then swings the loudspeaker at a constant speed in a horizontal circle above his head.
An observer, standing a large distance away from the loudspeaker, hears sound of maximum frequency 1640 Hz. The speed of sound in air is 330 ms$^{-1}$.
(i) Determine the speed of the loudspeaker. [2]
(ii) Describe and explain, qualitatively, the variation in the frequency of the sound heard by the observer. [2]
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(a) State what is meant by the $\textit{diffraction}$ of a wave. [2]
(b) Laser light of wavelength 500 nm is incident normally on a diffraction grating. The resulting diffraction pattern has diffraction maxima up to and including the fourth-order maximum.
Calculate, for the diffraction grating, the minimum possible line spacing. [3]
(c) The light in (b) is now replaced with red light. State and explain whether this is likely to result in the formation of a fifth-order diffraction maximum. [2]
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(a) Define electric potential difference \( (p.d.) \).
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.............................................................................................................................. [1]
(b) A battery of electromotive force \( (\text{e.m.f.}) \) 14 V and negligible internal resistance is connected to a resistor network, as shown in Fig. 6.1.
Fig. 6.1
\( R_1 \) and \( R_2 \) are fixed resistors of resistances 6.0 \( \Omega \) and 12 \( \Omega \) respectively. \( R_3 \) is a variable resistor.
Switch \( S \) is closed.
(i) Calculate the current in the battery when the resistance of \( R_3 \) is set
1. at zero,
current = ................................................ A [2]
2. at 24 \( \Omega \).
current = ................................................ A [2]
(ii) Use your answers in (b)(i) to calculate the change in the total power produced by the battery when the resistance of \( R_3 \) is changed from zero to 24 \( \Omega \).
change in power = ................................................ W [2]
(c) Switch \( S \) in Fig. 6.1 is now opened.
Resistors \( R_1 \) and \( R_2 \) are made from metal wires. Some data for these resistors are shown in Fig. 6.2.
[Table_1]
Fig. 6.2
Determine the ratio
\( \frac{\text{average drift speed of free electrons in } R_1}{\text{average drift speed of free electrons in } R_2} \)
ratio = ................................................ [2]
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(a) State one difference between a hadron and a lepton.
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(b) (i) State the quark composition of a proton and of a neutron.
proton: ....................................................................................................................................
neutron: ..................................................................................................................................
[2]
(ii) Use your answer in (i) to determine the quark composition of an $\alpha$-particle.
quark composition: ............................................................................................................[1]
(c) The results of the $\alpha$-particle scattering experiment provide evidence for the structure of the atom.
result 1: The vast majority of $\alpha$-particles pass straight through the metal foil or are deviated by small angles.
result 2: A very small minority of $\alpha$-particles are scattered through angles greater than $90^\circ$.
State what may be inferred from
(i) result 1,
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(ii) result 2.
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