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(a) Compare scalar and vector quantities. [2]
(b) The radius of a small sphere is determined from a measurement of the volume of the sphere. The sphere is submerged in water, displacing some of the water into a measuring cylinder as shown in Fig. 1.1.
The measured volume of displaced water is (28.0 ± 0.5)cm³.
Calculate:
(i) the radius, in cm, of the sphere. [1]
(ii) the percentage uncertainty in the radius of the sphere. [2]
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A hot-air balloon floats just above the ground. The balloon is stationary and is held in place by a vertical rope, as shown in Fig. 2.1.
The balloon has a weight $W$ of $3.39 \times 10^4 \text{N}$. The tension $T$ in the rope is $4.00 \times 10^2 \text{N}$. Upthrust $U$ acts on the balloon. The density of the surrounding air is $1.23 \text{kg m}^{-3}$.
(a) (i) On Fig. 2.1, draw labelled arrows to show the directions of the three forces acting on the balloon. [2]
(ii) Calculate the volume, to three significant figures, of the balloon. [3]
(iii) The balloon is released from the rope. Calculate the initial acceleration of the balloon. [3]
(b) The balloon is stationary at a height of $500 \text{m}$ above the ground. A tennis ball is released from rest and falls vertically from the balloon.
A passenger in the balloon uses the equation $v^2 = u^2 + 2as$ to calculate that the ball will be travelling at a speed of approximately $100 \text{ms}^{-1}$ when it hits the ground.
Explain why the actual speed of the ball will be much lower than $100 \text{ms}^{-1}$ when it hits the ground.[3]
(c) Before the balloon is released, the rope holding the balloon has a strain of $2.4 \times 10^{-5}$. The rope has an unstretched length of $2.5 \text{m}$. The rope obeys Hooke's law.
(i) Show that the extension of the rope is $6.0 \times 10^{-5} \text{m}$. [1]
(ii) Calculate the elastic potential energy $E_P$ of the rope.[2]
(iii) The rope holding the balloon is replaced with a new one of the same original length and cross-sectional area. The tension is unchanged and the new rope also obeys Hooke’s law.
The new rope is made from a material of a lower Young modulus.
State and explain the effect of the lower Young modulus on the elastic potential energy of the rope. [2]
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A trolley A moves along a horizontal surface at a constant velocity towards another trolley B which is moving at a lower constant speed in the same direction. Fig. 3.1 shows the trolleys at time $t = 0$.
Table 3.1 shows data for the trolleys.
The two trolleys collide elastically and then separate. Resistive forces are negligible.
Fig. 3.2 shows the variation with time $t$ of the velocity $v$ for trolley B.
(a) State what is represented by the area under a velocity–time graph. [1]
(b) Use Table 3.1 and Fig. 3.2 to determine:
(i) the acceleration of trolley B during the collision [2]
(ii) the magnitude and direction of the final velocity of trolley A. [3]
(c) On Fig. 3.2, sketch the variation of the velocity of trolley A with time t from t = 0 to t = 0.50s. [3]
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(a) State the principle of superposition. [2]
(b) Coherent light is incident normally on two identical slits X and Y. The diffracted light emerging from the slits superposes to produce an interference pattern on a screen positioned at a distance of 1.9 m from the slits.
Fig. 4.1 shows the arrangement and the central part of the interference pattern of bright and dark fringes formed on the screen.
The separation of the slits is 0.65 mm. The distance between the centres of adjacent bright fringes is 1.7 mm.
Calculate the wavelength $\lambda$ of the light. [3]
(c) Light waves from slits X and Y in (b) arrive at a point between adjacent bright fringes on the screen. Fig. 4.2 shows the variation of displacement with time for the waves arriving at the point where they meet.
A student makes two statements about the waves at this point:
Statement 1: 'The phase difference between the waves is 90$^\circ$.'
Statement 2: 'The amplitude of the resultant wave is zero.'
(i) Explain how statement 1 is correct. [1]
(ii) State and explain whether statement 2 is correct. [1]
(d) The width of each slit in (b) is decreased by the same amount. There is no change to the separation of the slits.
Describe and explain the effect, if any, of this change on the appearance of the interference pattern. [2]
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A train travels at a constant high speed along a straight horizontal track towards an observer standing adjacent to the track, as shown in Fig. 5.1.
The train sounds its horn continuously as it approaches the observer, from time $t = 0$ until it is well past the observer at time $t = t_2$. The train passes the observer at time $t = t_1$.
The horn emits a sound wave of constant frequency $f_s$.
(a) On Fig. 5.2, sketch the variation of the frequency of sound heard by the observer with time $t$, from time $t = 0$ to $t = t_2$. [1]
(b) At a particular time, the sound waves at the observer have an intensity of $4.7 \times 10^{-3} \, \text{W m}^{-2}$. The waves at the observer are incident at right angles on a circular detector of radius $2.8 \, \text{cm}$.
Calculate the power $P$ of the waves incident on the detector. [3]
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A battery is connected in a circuit with a light-dependent resistor (LDR), two fixed resistors and a voltmeter, as shown in Fig. 6.1.
[Image_1: Fig. 6.1 Circuit diagram]
The battery has an electromotive force (e.m.f.) of 25V and negligible internal resistance. The resistors have resistances of 320Ω and 240Ω.
(a) The voltmeter displays a reading of 16V.
(i) Show that the current in the battery is 0.050A. [1]
(ii) Calculate the resistance of the LDR.
resistance = .............................................. Ω [3]
(iii) Determine the ratio
\[\text{ratio} = \frac{\text{power dissipated in the LDR}}{\text{power dissipated in the 240Ω resistor}}\]
ratio = .............................................. [2]
(b) The intensity of the light incident on the LDR increases.
State and explain what happens to the voltmeter reading.
..............................................................................................................................
..............................................................................................................................
.............................................................................................................................. [3]
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(a) The results of the $\alpha$-particle scattering experiment led to the development of the nuclear model for the atom.
State the results that suggested that most of the mass of the atom is concentrated in a very small region and most of the atom is empty space.
.............................................................................................................................................................................................
.............................................................................................................................................................................................
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............................................................................................................................................................................................. [2]
(b) State the composition of $\gamma$-radiation.
............................................................................................................................................................................................. [1]
(c) Table 7.1 lists the names of three particles and possible classifications for them.
[Table_1: Contains particle name and classification into baryon, hadron, lepton]
Complete Table 7.1 by placing ticks (✔) in the boxes to indicate the classifications that apply to each particle. [2]
(d) The discovery of a particle with an unusual charge was an important step in the development of the theory of quarks. The particle is a hadron with a mass of $2.19 \times 10^{-27}$ kg and a charge of $+2e$, where $e$ is the elementary charge.
(i) Calculate the mass, in $u$, of the particle. Give your answer to three significant figures.
mass = .................................................. $u$ [1]
(ii) Determine a possible quark composition of a hadron with a charge of $+2e$.
Explain your reasoning. [2]
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