2023 Cambridge IAS-Level Physics (9702) Practice Paper with Answers

Two wires, X and Y, are made of the same metal. Wire X has length L and diameter d. Wire Y has length 2L and diameter 2d. Both wires are suspended vertically from a rigid support and each supports the same load F at its lower end. What is the ratio of the strain energy stored in wire X to the strain energy stored in wire Y?

A uniform plank of length 3.0 m and weight 120 N rests horizontally on two supports. One support is at the left end of the plank, and the other support is 1.0 m from the right end of the plank. A metal block of weight 200 N is placed on the plank at a distance x from the left end. The upward force exerted on the plank by the left support is 100 N. What is the distance x?

A battery of electromotive force (e.m.f.) E and internal resistance r is connected across a variable resistor. The potential difference across the variable resistor is V and the current in the circuit is I. Which graph would be a straight line with a gradient equal to -r?

A uniform metal wire of resistance 12.0 ohms is stretched uniformly to three times its original length. The volume and density of the wire do not change during the stretching. What is the resistance of the stretched wire?

A tube closed at one end has a fundamental frequency of 240 Hz. The speed of sound in air is 340 m s^-1. Which frequency is NOT a harmonic of this tube?

A toy car of mass 0.50 kg is released from rest at the top of a rough slope of height 2.0 m. The car reaches the bottom of the slope with a speed of 4.0 m s^-1. How much work is done against the frictional forces during the descent?

Trolley P of mass 3m moves with a velocity v along a frictionless horizontal track. It collides with a stationary trolley Q of mass m. After the collision, the two trolleys stick together and move with a common velocity. What fraction of the initial kinetic energy is lost as thermal energy during the collision?

The resistivity rho of a wire is determined using the formula rho = R * pi * d^2 / (4 * L). The measured values and their percentage uncertainties are shown: resistance R has an uncertainty of 3.0%, diameter d has an uncertainty of 2.0%, and length L has an uncertainty of 1.5%. What is the percentage uncertainty in the calculated value of the resistivity rho?

The resistivity \(\rho\) of a metal wire is determined using the equation \(\rho = \frac{R \pi d^2}{4 L}\). The measurements obtained are: resistance \(R = (25.0 \pm 0.5)\ \Omega\), diameter \(d = (0.80 \pm 0.02)\text{ mm}\), and length \(L = (1.50 \pm 0.03)\text{ m}\). What is the percentage uncertainty in the calculated value of the resistivity?

A uniform horizontal shelf of length \(1.2\text{ m}\) and weight \(36\text{ N}\) is attached to a wall by a frictionless hinge at point A. The shelf is held horizontal by a wire connected between the outer end of the shelf (point B) and a point C on the wall, which is vertically above A. The distance AC is \(0.9\text{ m}\). What is the tension in the wire?

A steel wire X has length \(L\) and diameter \(d\). Another steel wire Y made of the same material has length \(2L\) and diameter \(2d\). Both wires obey Hooke's law and support the same vertical load \(F\). What is the ratio \(\frac{\text{elastic potential energy in X}}{\text{elastic potential energy in Y}}\)?

A stationary wave is established on a stretched string of length \(1.20\text{ m}\) which is fixed at both ends. The string vibrates in its third harmonic with a frequency of \(150\text{ Hz}\). What is the speed of the transverse waves on the string?

A cylindrical metal wire of length \(L\) and uniform cross-sectional area \(A\) has resistance \(R\). The wire is stretched at constant volume so that its length increases by \(10\%\). Assuming the resistivity of the metal remains unchanged, what is the new resistance of the wire?

A battery of electromotive force (e.m.f.) \(12\text{ V}\) and internal resistance \(r\) is connected to a variable resistor of resistance \(R\). When \(R = 4.0\ \Omega\), the terminal potential difference across the battery is \(8.0\text{ V}\). What is the terminal potential difference when \(R\) is increased to \(10.0\ \Omega\)?

A block of mass \(0.50\text{ kg}\) is launched up a rough inclined plane with an initial speed of \(6.0\text{ m s}^{-1}\). The block travels a distance of \(2.0\text{ m}\) along the slope, rising to a vertical height of \(1.2\text{ m}\) before coming to rest. What is the average frictional force acting on the block during its motion up the slope?

A nucleus of polonium-218 (\(^{218}_{84}\text{Po}\)) decays through a series of alpha (\(\alpha\)) and beta-minus (\(\beta^-\)) emissions to a stable isotope of lead-206 (\(^{206}_{82}\text{Pb}\)). How many \(\alpha\) and \(\beta^-\)-particles are emitted in this decay series?

Two wires, X and Y, made of the same metal, are joined end-to-end and stretched by a constant tensile force. Wire X has length \(L\) and diameter \(d\). Wire Y has length \(2L\) and diameter \(2d\). What is the ratio \(\frac{\text{elastic potential energy stored in X}}{\text{elastic potential energy stored in Y}}\)?

A uniform beam of weight \(W\) and length \(L\) is supported by a pivot located at a distance of \(\frac{L}{3}\) from its left end. A block of weight \(W\) is hung from the extreme left end. A vertical downward force \(F\) is applied at the extreme right end to keep the beam in horizontal equilibrium. What is the magnitude of the force \(F\) in terms of \(W\)?

A cell of electromotive force (e.m.f.) \(6.0\text{ V}\) and internal resistance \(1.0\ \Omega\) is connected in series with a \(2.0\ \Omega\) fixed resistor and a thermistor. As the temperature of the thermistor increases, its resistance decreases from \(3.0\ \Omega\) to \(1.0\ \Omega\). What are the initial and final values of the potential difference across the thermistor?

Two cylindrical conductors, P and Q, are made of the same metal and have the same mass. Conductor Q has twice the length of conductor P. What is the ratio \(\frac{\text{resistance of Q}}{\text{resistance of P}}\)?

A stationary wave is set up in an air column inside a pipe of length \(0.85\text{ m}\) that is closed at one end and open at the other. The speed of sound in air is \(340\text{ m s}^{-1}\). Which of the following frequencies is NOT a possible resonant frequency of this air column?

The density \(\rho\) of a solid cylinder of mass \(m\), diameter \(d\), and height \(h\) is determined using the equation \(\rho = \frac{4m}{\pi d^2 h}\). The measurements obtained are: \(m = (120.0 \pm 1.2)\text{ g}\), \(d = (2.00 \pm 0.04)\text{ mm}\), and \(h = (5.0 \pm 0.1)\text{ cm}\). What is the percentage uncertainty in the calculated value of \(\rho\)?

Unpolarised light of intensity \(I_0\) is incident on a pair of polarising filters. The angle between the transmission axes of the two filters is \(60^\circ\). What is the intensity of the light emerging from the second filter?

A free proton decays via \(\beta^+\) decay to form a neutron, a positron, and an electron neutrino. Which row correctly identifies the change in quark flavour and the leptons produced during this process?

The resistivity \(\rho\) of a uniform metal wire is calculated using the formula \(\rho = \frac{R \pi d^2}{4 L}\). The percentage uncertainties in the measurements are: resistance \(R\) is \(2\%\), diameter \(d\) is \(2\%\), and length \(L\) is \(1\%\). What is the percentage uncertainty in the calculated value of the resistivity?

Two trolleys, X and Y, are placed on a horizontal frictionless track. Trolley X has mass \(2m\) and moves with velocity \(v\) towards trolley Y, of mass \(3m\), which is initially at rest. The trolleys collide and stick together. What percentage of the initial kinetic energy is lost as thermal energy and sound during the collision?

A block of mass \(0.50\text{ kg}\) is launched up a constant slope of angle \(30^\circ\) to the horizontal with an initial kinetic energy of \(20\text{ J}\). The block travels a distance of \(2.0\text{ m}\) along the slope before coming to rest. What is the average resistive force acting on the block during its ascent?

Two wires, X and Y, are made of the same material and are suspended vertically from a ceiling. Wire X has length \(L\) and diameter \(d\). Wire Y has length \(2L\) and diameter \(2d\). If both wires support equal loads, what is the ratio of the extension of wire X to the extension of wire Y?

A uniform beam of weight \(120\text{ N}\) and length \(3.0\text{ m}\) is pivoted at one end. The beam is held horizontally in equilibrium by a cable attached to the other end. The cable makes an angle of \(30^\circ\) with the horizontal beam. What is the tension in the cable?

A stationary wave is set up on a stretched string of length \(1.2\text{ m}\) fixed at both ends. The string vibrates in its third harmonic. What is the distance between a node and an adjacent antinode?

A uniform metal wire has resistance \(R\). The wire is stretched until its length is doubled. Assuming that the volume and resistivity of the metal do not change, what is the new resistance of the wire?

A battery of electromotive force (e.m.f.) \(E\) and internal resistance \(r\) is connected in series with a variable resistor. When the resistance of the variable resistor is varied, the current in the circuit is \(I\) and the potential difference across the battery terminals is \(V\). A graph is plotted with \(V\) on the vertical axis and \(I\) on the horizontal axis. What is the gradient of this graph?

Two wires, \(X\) and \(Y\), are made of the same material. Wire \(X\) has length \(L\) and diameter \(d\). Wire \(Y\) has length \(2L\) and diameter \(2d\). Both wires obey Hooke's law. They are extended by equal tensile forces. What is the ratio of the elastic potential energy stored in wire \(X\) to that stored in wire \(Y\)?

A uniform bar of length \(2.0\text{ m}\) and weight \(40\text{ N}\) is supported horizontally by a pivot at a distance of \(0.40\text{ m}\) from its left end. A vertical string attached to the right end of the bar exerts an upward force of \(10\text{ N}\). A load of weight \(W\) is suspended from the extreme left end of the bar so that the bar remains in horizontal equilibrium. What is the weight \(W\)?

A battery of electromotive force (e.m.f.) \(E\) and internal resistance \(r\) is connected in series with a variable resistor. A voltmeter of infinite resistance is connected across the terminals of the battery.

The resistance of the variable resistor is varied, and the terminal potential difference \(V\) across the battery is recorded for different currents \(I\). A graph is plotted of \(V\) on the vertical axis against \(I\) on the horizontal axis.

Which statement about this graph is correct?

A cylindrical wire of length \(L\) and cross-sectional area \(A\) has a resistance \(R\). The wire is stretched uniformly so that its length increases by \(10\%\) while its volume remains constant. What is the new resistance of the wire in terms of \(R\)?

A stationary wave of wavelength \(\lambda\) is set up on a stretched string. Two points, \(X\) and \(Y\), on the string are oscillating. The distance between \(X\) and \(Y\) is exactly \(\frac{1}{3}\lambda\), and there is no node between them. What is the phase difference between the oscillations of \(X\) and \(Y\)?

A block of mass \(2.0\text{ kg}\) is pushed up a rough slope inclined at an angle of \(30^\circ\) to the horizontal. An average frictional force of \(5.0\text{ N}\) acts on the block parallel to the slope. The block is pushed with a constant force of \(20\text{ N}\) parallel to the slope for a distance of \(4.0\text{ m}\). What is the increase in the kinetic energy of the block over this distance?

Unpolarised light of intensity \(I_0\) is incident on a polarizing filter. The light transmitted by this first filter then passes through a second polarizing filter (the analyser). The transmission axis of the analyser is at an angle of \(60^\circ\) to the transmission axis of the first filter. What is the intensity of the light emerging from the analyser?

An experimenter determines the acceleration of free fall \(g\) by measuring the period \(T\) of a simple pendulum of length \(L\). The equation used is:

\(g = \frac{4\pi^2 L}{T^2}\)

The percentage uncertainty in the measurement of \(L\) is \(1.5\%\). The percentage uncertainty in the measurement of \(T\) is \(2.0\%\).

What is the percentage uncertainty in the calculated value of \(g\)?

A copper wire of original length \(2.40\text{ m}\) and cross-sectional area \(3.2 \times 10^{-7}\text{ m}^2\) is suspended vertically. A load of \(48\text{ N}\) is applied to the free end, causing an elastic extension. The Young modulus of copper is \(1.2 \times 10^{11}\text{ Pa}\). (a) Define the term tensile strain. [1.5 marks] (b) Calculate: (i) the stress in the wire due to the load, [2 marks] (ii) the extension produced by this load. [2 marks] (c) State and explain how the extension would differ if a steel wire of the same initial length and diameter, but with a Young modulus of \(2.0 \times 10^{11}\text{ Pa}\), were used under the same load. [2 marks]

A non-uniform wooden plank AB of length \(3.0\text{ m}\) and weight \(120\text{ N}\) is supported horizontally by two vertical ropes. One rope is attached at end A and the other rope is attached at a distance of \(0.60\text{ m}\) from end B. The tension in the rope at end A is \(40\text{ N}\). (a) State the two conditions required for a rigid body to be in equilibrium. [2 marks] (b) Calculate: (i) the tension in the second rope, [1.5 marks] (ii) the distance of the centre of gravity of the plank from end A. [4 marks]

A cell of electromotive force (e.m.f.) \(E = 6.0\text{ V}\) and internal resistance \(r = 1.5\ \Omega\) is connected in series with a resistor R and a switch. A high-resistance voltmeter is connected across the terminals of the cell. (a) Explain what is meant by the internal resistance of a cell. [1.5 marks] (b) When the switch is open, the reading on the voltmeter is \(V_1\). When the switch is closed, the reading is \(V_2 = 4.8\text{ V}\). (i) State the value of \(V_1\). [1 mark] (ii) Calculate the current in the circuit when the switch is closed. [2 marks] (iii) Calculate the resistance of resistor R. [3 marks]

A uniform wire X of length \(1.5\text{ m}\) and diameter \(0.40\text{ mm}\) has a resistance of \(6.4\ \Omega\). (a) Show that the resistivity of the material of wire X is approximately \(5.4 \times 10^{-7}\ \Omega\text{ m}\). [3 marks] (b) A second wire Y is made of the same material as wire X. Wire Y has twice the length and half the diameter of wire X. Calculate: (i) the cross-sectional area of wire Y, [2.5 marks] (ii) the resistance of wire Y. [2 marks]

A tuning fork of frequency \(340\text{ Hz}\) is held above the open end of a vertical tube that is closed at the bottom by water. The length of the air column in the tube is gradually increased from zero by lowering the water level. A loud sound (resonance) is first heard when the length of the air column is \(24.0\text{ cm}\). (a) Explain how a stationary wave is formed in the air column. [2.5 marks] (b) Calculate: (i) the speed of sound in the air, [3 marks] (ii) the length of the air column when the next resonance is heard. [2 marks]

A block of mass \(0.50\text{ kg}\) is released from rest at the top of a rough ramp inclined at \(30^\circ\) to the horizontal. The length of the ramp is \(2.0\text{ m}\). The block slides down the ramp and reaches the bottom with a speed of \(3.6\text{ m s}^{-1}\). (a) Calculate, for the block's motion from the top to the bottom of the ramp: (i) the loss in gravitational potential energy, [2 marks] (ii) the gain in kinetic energy. [2 marks] (b) Calculate the work done against friction as the block slides down the ramp. [1.5 marks] (c) Determine the average frictional force acting on the block. [2 marks]

A nucleus of bismuth-212 (\(_{83}^{212}\text{Bi}\)) is unstable and can decay by emitting either an \(\alpha\)-particle to form a nucleus of thallium (\(\text{Tl}\)) or a \(\beta^-\)-particle to form a nucleus of polonium (\(\text{Po}\)). (a) Write a nuclear equation to represent: (i) the \(\alpha\)-decay of bismuth-212, [2 marks] (ii) the \(\beta^-\)-decay of bismuth-212. [2.5 marks] (b) During \(\beta^-\)-decay, a neutron in the nucleus decays into a proton. State the change in quark composition of this nucleon. [1 mark] (c) A detector measures the activity of a sample of bismuth-212. Explain why the measured count rate is always less than the actual activity of the sample. [2 marks]

A student determines the density \(\rho\) of a metal cylinder. The following measurements are made: mass \(m = 48.2 \pm 0.1\text{ g}\), diameter \(d = 1.24 \pm 0.02\text{ cm}\), length \(L = 5.80 \pm 0.05\text{ cm}\). (a) Distinguish between systematic errors and random errors. [2 marks] (b) Calculate: (i) the percentage uncertainty in the volume of the cylinder, [3.5 marks] (ii) the density \(\rho\), with its absolute uncertainty, in \(\text{g cm}^{-3}\). [2 marks]

Answer all questions. Record all your observations in the spaces provided as soon as these observations are made. In this experiment, you will investigate how the deflection of a clamped metre rule (acting as a cantilever) depends on the length of the overhanging section. Apparatus: Metre rule clamped to a bench (to act as the cantilever), G-clamp and wooden blocks, Mass hanger of mass \(M = 500\text{ g}\), Second vertical metre rule to measure heights above the floor, Set square. (a)(i) Set up the apparatus where a horizontal metre rule is clamped to the edge of a bench. Adjust the position of the rule in the clamp so that the projecting length \(L\) is \(60.0\text{ cm}\). Record \(L\). (ii) With no mass suspended from the free end of the rule, measure the vertical height \(h_0\) of the bottom edge of the free end of the rule above the floor. Use the set square to ensure that the vertical rule is perpendicular to the floor. Record \(h_0\). (iii) Suspend the mass \(M = 500\text{ g}\) from the free end of the rule. Measure the new vertical height \(h\) of the bottom edge of the free end of the rule above the floor. Record \(h\). (iv) Calculate the deflection \(y\), where \(y = h_0 - h\). (b) Change \(L\) and repeat (a)(ii), (a)(iii) and (a)(iv) to obtain six sets of values of \(L\), \(h_0\), \(h\) and \(y\). The values of \(L\) should be in the range \(50.0\text{ cm} \le L \le 80.0\text{ cm}\). In your table of results, include calculated values of \(L^2\) and \(y/L\). (c)(i) Plot a graph of \(y/L\) on the y-axis against \(L^2\) on the x-axis. (ii) Draw the straight line of best fit. (d) Determine the gradient and y-intercept of this line. (e) The quantities \(y\) and \(L\) are related by the equation: \(\frac{y}{L} = p L^2 + q\) where \(p\) and \(q\) are constants. Using your answers from (d), determine values for \(p\) and \(q\). Include appropriate units for both constants.

Answer all questions. Record all your observations in the spaces provided as soon as these observations are made. In this experiment, you will investigate the tipping point of an overhanging metre rule to determine its mass. Apparatus: Metre rule (wooden, of mass \(M\)), Flat bench or table with a straight, horizontal edge, A mass \(m = 200\text{ g}\), Small piece of tape. (a)(i) Place the metre rule on the flat table surface perpendicular to the edge of the table. Let a length \(x\) of the rule project beyond the edge of the table. Set \(x = 30.0\text{ cm}\). Securely tape a mass \(m = 200\text{ g}\) to the rule. The mass should be on the overhanging section, at a distance \(d\) from the table edge. Adjust the position of the mass along the overhanging section until the rule is just on the point of tipping (the end on the table is just about to lift). Measure the distance \(d\) from the table edge to the center of the mass \(m\). Record \(d\). (ii) Repeat your measurements to find an average value of \(d\). Record the average \(d\). (iii) Estimate the percentage uncertainty in your average value of \(d\). Show your working. (b) Describe the technique you used to determine the tipping point as precisely as possible. (c)(i) Change \(x\) to \(40.0\text{ cm}\). Repeat (a)(i) and (a)(ii) to find the new average value of \(d\). Record \(x\) and average \(d\). (ii) Check if the trend is correct (\(d\) is smaller for \(x = 40.0\text{ cm}\) than for \(x = 30.0\text{ cm}\)). (d) The relationship between \(d\), \(x\), and the mass \(M\) of the rule is given by: \(M = \frac{m d}{50.0 - x}\) where \(m = 200\text{ g}\). (i) Calculate the value of \(M\) for \(x = 30.0\text{ cm}\) and \(x = 40.0\text{ cm}\). Include appropriate units. (ii) State the number of significant figures you have chosen for your values of \(M\) and explain your choice. (e) It is suggested that the percentage difference between your two values of \(M\) is within the limits of experimental accuracy. State whether your results support this suggestion. Justify your conclusion with a calculation. (f) Describe four sources of uncertainty or limitations of the procedure in this experiment. (g) Describe four improvements that could be made to this experiment to address the sources of uncertainty or limitations described in (f).