Question 1
What represents a vector quantity?
(B) \(2\,\mathrm{kg}\) decrease
(C) \(3\,\mathrm{K}\) cooler
(D) \(4\,\mathrm{s}\) later
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
A vector quantity has both magnitude and direction.
\(1\,\mathrm{N}\) upwards specifies both the magnitude of the force and its direction.
The other options do not represent vector quantities.
Therefore, the correct answer is (A).
Question 2
What is a reasonable estimate of the current in an electric kettle that is in use?
(B) \(8\,\mathrm{mA}\)
(C) \(8\,\mathrm{A}\)
(D) \(8\,\mathrm{kA}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
An electric kettle typically has a power of about \(2\,\mathrm{kW}\).
Using \(P=VI\),
\(I=\dfrac{P}{V}\approx\dfrac{2000}{230}\approx8.7\,\mathrm{A}\).
A current of about \(8\,\mathrm{A}\) is therefore a reasonable estimate.
Therefore, the correct answer is (C).
Question 3
Which statement about errors in measurements is correct?
(B) A precise set of measurements always has a small systematic error.
(C) A random error can be reduced by taking an average of several measurements.
(D) A systematic error creates a random set of measurements spread out about the true value.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Random errors cause measurements to scatter about the true value.
Taking repeated measurements and calculating the average reduces the effect of random errors.
Systematic errors shift all measurements in the same direction and cannot be removed by averaging.
Therefore, the correct answer is (C).
Question 4
A sample of material has cross-sectional area \(A\) and length \(L\). The temperatures at the two sides of the sample are \(T_1\) and \(T_2\). Thermal energy \(Q\) is transferred through the sample in time \(t\).
These quantities are related by
\( \dfrac{Q}{t}=\dfrac{kA(T_1-T_2)}{L} \)
where \(k\) is a constant.
What are the SI base units of \(k\)?
(B) \(\mathrm{kg\,m\,s^{-3}\,K^{-1}}\)
(C) \(\mathrm{kg\,m\,s^{-1}\,^{\circ}C^{-1}}\)
(D) \(\mathrm{kg\,m\,s^{-1}\,K^{-1}}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Since
\( \dfrac{Q}{t} \) has units of power \(=\mathrm{W}=\mathrm{kg\,m^2\,s^{-3}} \),
\( k=\dfrac{(Q/t)L}{A(T_1-T_2)} \).
Hence,
\(k=\dfrac{\mathrm{kg\,m^2\,s^{-3}}\times\mathrm{m}}{\mathrm{m^2}\times\mathrm{K}}=\mathrm{kg\,m\,s^{-3}\,K^{-1}}\).
Therefore, the correct answer is (B).
Question 5
The graph shows the variation of velocity with time \(t\) of an object moving in a straight line.
At \(t=0\), the displacement of the object is zero.
What is the displacement of the object at \(t=20\,\mathrm{s}\)?
(B) \(21\,\mathrm{m}\)
(C) \(24\,\mathrm{m}\)
(D) \(27\,\mathrm{m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Displacement is the area under the velocity-time graph.
From \(0\) to \(8\,\mathrm{s}\):
\(A_1=\dfrac{1}{2}\times8\times3=12\,\mathrm{m}\).
From \(8\) to \(16\,\mathrm{s}\):
\(A_2=\dfrac{1}{2}\times8\times3=12\,\mathrm{m}\).
From \(16\) to \(20\,\mathrm{s}\):
\(A_3=-\dfrac{1}{2}\times4\times1.5=-3\,\mathrm{m}\).
Total displacement:
\(12+12-3=21\,\mathrm{m}\).
Therefore, the correct answer is (B).
Question 6
A science museum designs an experiment to show the fall of a feather in a vertical glass vacuum tube.
The time of fall from rest in the vacuum is to be close to \(0.5\,\mathrm{s}\).
Which length of tube is required?
(B) \(2.5\,\mathrm{m}\)
(C) \(4.9\,\mathrm{m}\)
(D) \(9.8\,\mathrm{m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
For free fall from rest,
\(s=\dfrac{1}{2}gt^2\).
Substituting \(g=9.8\,\mathrm{m\,s^{-2}}\) and \(t=0.5\,\mathrm{s}\),
\(s=\dfrac{1}{2}\times9.8\times(0.5)^2\)
\(=4.9\times0.25=1.225\,\mathrm{m}\).
This is approximately \(1.2\,\mathrm{m}\).
Therefore, the correct answer is (A).
Question 7
Two coins are projected from a horizontal table at the same initial speed \(u\).
Coin X is projected horizontally.
Coin Y is projected upwards at an angle of \(30^\circ\) to the horizontal.
Both coins hit the horizontal ground without bouncing.
Assume the air resistance on each coin is negligible.
Which statement about the motion of the coins is correct?
(B) Both coins travel the same vertical distance.
(C) Coin Y hits the ground before coin X.
(D) Coin Y has a smaller vertical acceleration.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Both coins start with the same initial speed and fall through the same vertical height.
Neglecting air resistance, mechanical energy is conserved.
Hence, for both coins,
\(v^2=u^2+2gh\),
where \(h\) is the height of the table.
Since \(u\) and \(h\) are the same for both coins, they strike the ground with the same speed.
Coin Y remains in the air longer and both coins have the same downward acceleration \(g\).
Therefore, the correct answer is (A).
Question 8
Two spheres are released from rest at equal heights above the ground.
Both spheres reach terminal velocity.
One sphere has a larger density than the other.
Both spheres have equal volumes.
Which statement is correct while both spheres are at terminal velocity?
(B) The resultant forces on the spheres are equal.
(C) The velocities of the spheres are equal.
(D) The weights of the spheres are equal.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
At terminal velocity, the acceleration is zero.
Therefore, the resultant force on each sphere is zero:
\(\sum F=0\).
The sphere with the greater density has a greater mass and weight, so its drag force at terminal velocity is also greater.
Thus, the drag forces, terminal velocities and weights are not equal.
However, the resultant force on both spheres is the same, namely zero.
Therefore, the correct answer is (B).
Question 9
Which statement defines force?
(B) When a force acts on a body that is free to move, the force is the rate of change of momentum of the body.
(C) When a force acts on a body that is free to move, the force is the work done by the force divided by the distance moved by the body.
(D) When a force acts on a lever and causes a moment, the force is the moment divided by the perpendicular distance of the force from the pivot.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The fundamental definition of force is given by Newton’s second law:
\(F=\dfrac{\Delta p}{\Delta t}\),
where \(p\) is the momentum of the body.
The equation \(F=ma\) is a special case that applies when the mass is constant.
Therefore, the correct answer is (B).
Question 10
Four forces, all in the same plane, act on an object.
What could describe the motion of the object?
(B) It is moving in a straight line.
(C) It is moving with decreasing speed.
(D) It is moving with increasing momentum.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The horizontal forces are equal and opposite (\(20\,\mathrm{N}\)), and the vertical forces are also equal and opposite (\(12\,\mathrm{N}\)).
Hence, the resultant force on the object is zero.
With zero resultant force, the object has zero acceleration according to Newton’s first law.
The object could therefore remain at rest or move with constant velocity in a straight line.
Therefore, the correct answer is (B).
Question 11
A nucleus collides with a stationary nucleus in a vacuum. The diagrams show the paths of the nuclei before and after the collision.
No other particles are involved in the collision.
Which diagram is not possible?
(B) Diagram B
(C) Diagram C
(D) Diagram D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Momentum must be conserved in both the horizontal and vertical directions.
Initially, the total vertical momentum is zero because the incident nucleus moves horizontally and the other nucleus is stationary.
In diagram C, both nuclei move with downward components of momentum after the collision.
This gives a non-zero total downward momentum, violating conservation of momentum.
Therefore, diagram C is not possible.
Therefore, the correct answer is (C).
Question 12
A non-uniform bar \(PQ\) has length \(50\,\mathrm{cm}\) and weight \(200\,\mathrm{N}\).
A block of weight \(400\,\mathrm{N}\) is attached to the top of the bar at its centre.
The bar rests on horizontal ground.
A vertical force of \(360\,\mathrm{N}\) is now exerted upwards on the bar at \(Q\) and is just sufficient to lift end \(Q\) from the ground.
What is the distance from the centre of gravity of the bar to end \(P\)?
(B) \(0.10\,\mathrm{m}\)
(C) \(0.25\,\mathrm{m}\)
(D) \(0.40\,\mathrm{m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
When end \(Q\) is just lifted, the bar pivots about \(P\).
Taking moments about \(P\):
\(360\times0.50=400\times0.25+200\times x\).
\(180=100+200x\).
\(200x=80\).
\(x=0.40\,\mathrm{m}\).
Therefore, the centre of gravity of the bar is \(0.40\,\mathrm{m}\) from end \(P\).
Therefore, the correct answer is (D).
Question 13
What is the definition of density?
(B) mass of a unit volume
(C) mass per cubic metre
(D) mass per unit volume
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Density is defined as the mass per unit volume of a substance.
It is given by
\(\rho=\dfrac{m}{V}\).
The SI unit of density is \(\mathrm{kg\,m^{-3}}\).
Therefore, the correct answer is (D).
Question 14
A block is in equilibrium on a slope.
Which vector triangle represents the three forces acting on the block?
(B) Diagram B
(C) Diagram C
(D) Diagram D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The three forces acting on the block are:
\( \bullet \) the weight acting vertically downward,
\( \bullet \) the normal reaction perpendicular to the slope,
\( \bullet \) the frictional force parallel to the slope.
Since the block is in equilibrium, these three forces form a closed vector triangle.
Only diagram C shows the correct directions and a closed force triangle.
Therefore, the correct answer is (C).
Question 15
A measuring cylinder contains \(80\,\mathrm{cm^3}\) of a liquid.
The pressure due to the liquid at the \(60\,\mathrm{cm^3}\) mark is \(1200\,\mathrm{Pa}\).
What is the pressure due to the liquid at the base of the measuring cylinder?
(B) \(1600\,\mathrm{Pa}\)
(C) \(3600\,\mathrm{Pa}\)
(D) \(4800\,\mathrm{Pa}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Pressure in a liquid is proportional to the depth:
\(p=\rho gh\).
The pressure at the \(60\,\mathrm{cm^3}\) mark is due to the liquid above it, which has a volume of
\(80-60=20\,\mathrm{cm^3}\).
The base is below the full \(80\,\mathrm{cm^3}\) of liquid, which is four times the depth.
Hence,
\(p_{\text{base}}=4\times1200=4800\,\mathrm{Pa}\).
Therefore, the correct answer is (D).
Question 16
Four identical uniform blocks are spread on a table. Each block has mass \(m\) and thickness \(h\).
The acceleration due to free fall is \(g\).
How much work is done on the blocks in stacking them on top of one another?
(B) \(6mgh\)
(C) \(8mgh\)
(D) \(10mgh\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Initially, the centre of mass of each block is at a height of \(\dfrac{h}{2}\).
After stacking, the centres of mass are at
\(\dfrac{h}{2},\ \dfrac{3h}{2},\ \dfrac{5h}{2},\ \dfrac{7h}{2}\).
The increases in height are
\(0,\ h,\ 2h,\ 3h\).
The total increase in gravitational potential energy is
\(mgh(0+1+2+3)=6mgh\).
Therefore, the work done is \(6mgh\).
Therefore, the correct answer is (B).
Question 17
An electric motor uses \(1.7\,\mathrm{kW}\) of power when operating normally.
The efficiency of the motor is \(53\%\).
What is the useful output power of the motor?
(B) \(0.90\,\mathrm{kW}\)
(C) \(3.2\,\mathrm{kW}\)
(D) \(90\,\mathrm{kW}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Efficiency is given by
\(\eta=\dfrac{\text{useful output power}}{\text{input power}}\).
Hence,
\(\text{Useful output power}=0.53\times1.7=0.901\,\mathrm{kW}\).
\(\approx0.90\,\mathrm{kW}\).
Therefore, the correct answer is (B).
Question 18
A ball is released from rest and falls vertically to the ground.
The kinetic energy \(E_k\) of the ball varies as the height \(h\) of the ball above the ground changes.
Air resistance is negligible.
Which graph shows the variation of \(E_k\) with \(h\)?
(B) Graph B
(C) Graph C
(D) Graph D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
With negligible air resistance, mechanical energy is conserved.
The total mechanical energy is constant, so
\(E_k+E_p=\text{constant}\).
Since gravitational potential energy is
\(E_p=mgh\),
the kinetic energy is
\(E_k=\text{constant}-mgh\).
Thus, \(E_k\) decreases linearly with increasing height \(h\).
Therefore, the correct answer is (D).
Question 19
An object travelling with a speed of \(10\,\mathrm{m\,s^{-1}}\) has kinetic energy of \(1500\,\mathrm{J}\).
The speed of the object is increased to \(40\,\mathrm{m\,s^{-1}}\).
What is the new kinetic energy of the object?
(B) \(6000\,\mathrm{J}\)
(C) \(24\,000\,\mathrm{J}\)
(D) \(1\,350\,000\,\mathrm{J}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Kinetic energy is given by
\(E_k=\dfrac{1}{2}mv^2\).
Since the mass is unchanged,
\(E_k\propto v^2\).
The speed increases from \(10\,\mathrm{m\,s^{-1}}\) to \(40\,\mathrm{m\,s^{-1}}\), a factor of \(4\).
Therefore, the kinetic energy increases by a factor of \(4^2=16\).
\(E_{k,\text{new}}=1500\times16=24\,000\,\mathrm{J}\).
Therefore, the correct answer is (C).
Question 20
What are the units of stress, strain and the Young modulus?
| Stress | Strain | Young modulus | |
|---|---|---|---|
| (A) | newton | metre | pascal |
| (B) | newton | no unit | newton |
| (C) | pascal | metre | newton |
| (D) | pascal | no unit | pascal |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Stress is defined as
\(\sigma=\dfrac{F}{A}\),
so its SI unit is the pascal (\(\mathrm{Pa}\)).
Strain is
\(\varepsilon=\dfrac{\Delta L}{L}\),
which is a ratio and therefore has no unit.
Young modulus is
\(E=\dfrac{\text{stress}}{\text{strain}}\).
Since strain is dimensionless, Young modulus has the same unit as stress, namely the pascal.
Therefore, the correct answer is (D).
Question 21
The force-extension graph for a metal wire is shown.
Which quantity is represented by the area under the graph?
(B) temperature increase in the wire
(C) time taken for the wire to extend
(D) work done on the wire
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The work done in stretching a wire is
\(W=\int F\,\mathrm{d}x\).
Graphically, this is equal to the area under the force-extension graph.
For elastic deformation, this work is stored as elastic potential energy in the wire.
Therefore, the correct answer is (D).
Question 22
A wire of length \(L_0\) is attached at one end to a fixed point. A tensile force is applied to the other end so that the wire extends and has a new length \(L_1\).
What is the strain of the wire?
(B) \(L_1-L_0\)
(C) \( \left(\dfrac{L_1}{L_0}\right)+1 \)
(D) \(L_1+L_0\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Strain is defined as
\(\text{strain}=\dfrac{\text{extension}}{\text{original length}}\).
The extension of the wire is
\(L_1-L_0\).
Hence,
\(\text{strain}=\dfrac{L_1-L_0}{L_0}=\dfrac{L_1}{L_0}-1\).
Therefore, the correct answer is (A).
Question 23
A wire of length \(L\) is stretched to determine its limit of proportionality.
The graph shows the variation of the extension \(x\) with the force \(F\) applied to the wire.
The limit of proportionality is shown by point \(P\) on the graph.
The experiment is repeated with another wire of length \(2L\) but of the same material and the same diameter as the first wire.
Which point on the graph shows the limit of proportionality for the new wire?
(B) Point B
(C) Point C
(D) Point D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The limit of proportionality occurs at a fixed value of stress for a given material.
Since the two wires have the same material and the same cross-sectional area, the force at the limit of proportionality is unchanged.
The extension is
\(x=\dfrac{FL}{AE}\).
Doubling the length of the wire doubles the extension for the same applied force.
Hence, the new point has the same force as \(P\) but twice the extension.
This corresponds to point D.
Therefore, the correct answer is (D).
Question 24
The graph shows the variation with distance along the wave of the displacement of water particles at a particular instant in time for a transverse water wave.
\(P\), \(Q\) and \(R\) show the positions of three water particles in the wave.
Which particle has the greatest speed at the instant shown?
(B) particle \(P\)
(C) particle \(Q\)
(D) particle \(R\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
For a particle in simple harmonic motion, the speed is greatest when its displacement from the equilibrium position is zero.
The particle speed is given by
\(v=\omega\sqrt{A^2-y^2}\),
where \(y\) is the displacement from equilibrium.
Particle \(P\) is at maximum displacement, so its speed is zero.
Particle \(Q\) has an intermediate displacement.
Particle \(R\) is closest to the equilibrium position, so it has the greatest speed.
Therefore, the correct answer is (D).
Question 25
Which phenomenon is only associated with transverse waves?
(B) interference
(C) polarisation
(D) reflection
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Polarisation is the restriction of oscillations to a single plane.
Only transverse waves have oscillations perpendicular to the direction of propagation and can therefore be polarised.
Diffraction, interference and reflection occur for both transverse and longitudinal waves.
Therefore, the correct answer is (C).
Question 26
A wave is displayed on an oscilloscope.
The oscilloscope settings are:
time-base: \(300\,\mathrm{\mu s\,div^{-1}}\)
\(y\)-gain: \(40\,\mathrm{\mu V\,div^{-1}}\)
What is the frequency of the wave?
(B) \(950\,\mathrm{Hz}\)
(C) \(1100\,\mathrm{Hz}\)
(D) \(7100\,\mathrm{Hz}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
One complete cycle occupies approximately \(3.5\) horizontal divisions.
The period is
\(T=3.5\times300\,\mathrm{\mu s}=1050\,\mathrm{\mu s}=1.05\times10^{-3}\,\mathrm{s}\).
The frequency is
\(f=\dfrac{1}{T}=\dfrac{1}{1.05\times10^{-3}}\approx952\,\mathrm{Hz}\).
This is approximately \(950\,\mathrm{Hz}\).
Therefore, the correct answer is (B).
Question 27
An electromagnetic wave travelling in free space is not visible to the human eye.
What is a possible wavelength of the wave?
(B) \(6.2\times10^{-7}\,\mathrm{m}\)
(C) \(5.4\times10^{-6}\,\mathrm{cm}\)
(D) \(4.2\times10^{-4}\,\mathrm{mm}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Visible light has wavelengths approximately between
\(4.0\times10^{-7}\,\mathrm{m}\) and \(7.0\times10^{-7}\,\mathrm{m}\).
Converting each option to metres:
(A) \(4.5\times10^{-10}\,\mathrm{km}=4.5\times10^{-7}\,\mathrm{m}\) (visible)
(B) \(6.2\times10^{-7}\,\mathrm{m}\) (visible)
(C) \(5.4\times10^{-6}\,\mathrm{cm}=5.4\times10^{-8}\,\mathrm{m}\) (ultraviolet, not visible)
(D) \(4.2\times10^{-4}\,\mathrm{mm}=4.2\times10^{-7}\,\mathrm{m}\) (visible)
Therefore, the correct answer is (C).
Question 28
Electromagnetic waves of equal wavelengths are emitted from two sources, \(X\) and \(Y\). The waves are emitted from \(X\) and \(Y\) with a phase difference of \(180^\circ\).
A detector moves along a path that is parallel to the line \(XY\) and detects a pattern of intensity maxima and minima.
The diagram shows the arrangement of the sources and the path of the detector.
An intensity maximum is detected at point \(Z\). Length \(XZ\) is \(70\,\mathrm{cm}\) and length \(YZ\) is \(110\,\mathrm{cm}\).
What is a possible wavelength of the waves?
(B) \(16\,\mathrm{cm}\)
(C) \(20\,\mathrm{cm}\)
(D) \(40\,\mathrm{cm}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The path difference at \(Z\) is
\(\Delta =110-70=40\,\mathrm{cm}\).
Since the sources are \(180^\circ\) out of phase, a maximum occurs when
\(\Delta=\left(n+\dfrac{1}{2}\right)\lambda\),
where \(n=0,1,2,\ldots\).
Testing the options:
For \(\lambda=16\,\mathrm{cm}\),
\(40=2.5\times16=\dfrac{5}{2}\lambda\),
which satisfies the condition for constructive interference.
Therefore, the correct answer is (B).
Question 29
Two waves of the same type overlap.
When does the principle of superposition apply?
(B) only when the waves have the same amplitude
(C) only when the waves travel in opposite directions
(D) only when the waves have the same frequency
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The principle of superposition states that when two or more waves overlap, the resultant displacement at any point is the algebraic sum of the individual displacements.
This principle applies whenever waves of the same type overlap, regardless of their amplitudes, frequencies or directions of travel.
Therefore, the correct answer is (A).
Question 30
A ripple tank contains water at a constant depth.
A water wave of constant frequency travels towards a gap in a barrier placed in the ripple tank.
The gap is made smaller.
Which diagram represents the wave before and after the barrier?
(B) Diagram B
(C) Diagram C
(D) Diagram D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The speed of the wave remains constant because the water depth is unchanged.
The frequency is also constant, so the wavelength remains unchanged:
\(v=f\lambda\).
Making the gap smaller increases the amount of diffraction, causing the wavefronts to spread out more after passing through the gap.
Diagram D shows the same wavelength with greater spreading of the wavefronts.
Therefore, the correct answer is (D).
Question 31
Light of a single frequency from two coherent sources interferes to produce a pattern of bright and dark fringes on a screen.
Which change results in a larger fringe separation?
(B) increasing the distance between the two sources
(C) increasing the frequency of the light
(D) increasing the intensity of the light
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The fringe separation in Young’s double-slit experiment is
\(w=\dfrac{\lambda D}{a}\),
where:
\(D\) is the distance from the sources to the screen,
\(a\) is the separation of the sources,
\(\lambda\) is the wavelength of the light.
Increasing \(D\) increases the fringe separation.
Increasing the source separation or the frequency decreases the fringe separation, while changing the intensity does not affect the spacing.
Therefore, the correct answer is (A).
Question 32
The current \(I\) in a metallic conductor of cross-sectional area \(A\) is given by
\(I=Anve\)
where \(e\) is the elementary charge and \(v\) is the mean drift velocity of the conduction electrons.
What is represented by the letter \(n\) in the equation?
(B) number of conduction electrons per unit time
(C) number of conduction electrons per unit volume
(D) volume of conduction electrons
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The drift velocity equation is
\(I=Anve\),
where:
\(A\) is the cross-sectional area,
\(n\) is the number of free (conduction) electrons per unit volume,
\(v\) is the mean drift velocity,
and \(e\) is the elementary charge.
Therefore, the correct answer is (C).
Question 33
What cannot be the charge on a charge carrier?
(B) \(-3.2\times10^{-19}\,\mathrm{C}\)
(C) \(-2.4\times10^{-19}\,\mathrm{C}\)
(D) \(+3.2\times10^{-19}\,\mathrm{C}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Electric charge is quantised.
The charge on a particle must be an integer multiple of the elementary charge:
\(Q=ne\),
where \(e=1.6\times10^{-19}\,\mathrm{C}\) and \(n\) is an integer.
\(-2.4\times10^{-19}\,\mathrm{C}= -1.5e\), which is not an integer multiple of \(e\).
Therefore, the correct answer is (C).
Question 34
A steel wire with a length of \(2.20\,\mathrm{m}\) is connected to a battery as shown.
The reading on the voltmeter is \(1.50\,\mathrm{V}\) and the reading on the ammeter is \(4.90\,\mathrm{A}\).
The resistivity of steel is \(6.90\times10^{-7}\,\Omega\,\mathrm{m}\).
What is the diameter of the steel wire?
(B) \(3.52\times10^{-4}\,\mathrm{m}\)
(C) \(1.26\times10^{-3}\,\mathrm{m}\)
(D) \(2.51\times10^{-3}\,\mathrm{m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The resistance of the wire is
\(R=\dfrac{V}{I}=\dfrac{1.50}{4.90}=0.306\,\Omega\).
Using
\(R=\dfrac{\rho L}{A}\),
the cross-sectional area is
\(A=\dfrac{\rho L}{R}=\dfrac{(6.90\times10^{-7})(2.20)}{0.306}=4.96\times10^{-6}\,\mathrm{m^2}\).
Since
\(A=\dfrac{\pi d^2}{4}\),
\(d=\sqrt{\dfrac{4A}{\pi}}=\sqrt{\dfrac{4(4.96\times10^{-6})}{\pi}}=2.51\times10^{-3}\,\mathrm{m}\).
Therefore, the correct answer is (D).
Question 35
Two resistors of resistance \(R\) and two resistors of resistance \(3R\) are connected to a cell of e.m.f. \(8.0\,\mathrm{V}\) as shown.
The cell has negligible internal resistance.
What is the reading on the voltmeter?
(B) \(2.0\,\mathrm{V}\)
(C) \(4.0\,\mathrm{V}\)
(D) \(6.0\,\mathrm{V}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Each branch has a total resistance of
\(R+3R=4R\).
The \(8.0\,\mathrm{V}\) supply is shared across each branch.
In the top branch, the p.d. across \(R\) is
\(\dfrac{R}{4R}\times8.0=2.0\,\mathrm{V}\).
Thus the midpoint is at \(2.0\,\mathrm{V}\) below the left terminal.
In the bottom branch, the p.d. across \(3R\) is
\(\dfrac{3R}{4R}\times8.0=6.0\,\mathrm{V}\).
The potential difference between the two midpoints is
\(6.0-2.0=4.0\,\mathrm{V}\).
Therefore, the voltmeter reads \(4.0\,\mathrm{V}\).
Therefore, the correct answer is (C).
Question 36
A battery has an e.m.f. \(E\) and internal resistance \(r\). The battery delivers a current \(I\) to a variable resistor and the p.d. across its terminals is \(V\).
The variable resistor is adjusted so that \(I\) increases.
Why does \(V\) decrease?
(B) The internal resistance \(r\) increases.
(C) The p.d. across \(r\) increases.
(D) The resistance of the variable resistor increases.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The terminal potential difference is
\(V=E-Ir\).
When the current \(I\) increases, the voltage lost across the internal resistance is
\(Ir\).
Since \(Ir\) increases, the terminal p.d. \(V\) decreases.
The e.m.f. and the internal resistance remain constant.
Therefore, the correct answer is (C).
Question 37
An electrical device of fixed resistance \(20\,\Omega\) is connected in series with a variable resistor and a battery of e.m.f. \(16\,\mathrm{V}\) and negligible internal resistance.
The power dissipated in the electrical device is \(4.0\,\mathrm{W}\).
What is the resistance of the variable resistor?
(B) \(36\,\Omega\)
(C) \(44\,\Omega\)
(D) \(64\,\Omega\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The power dissipated in the \(20\,\Omega\) device is
\(P=I^2R\).
Hence,
\(I=\sqrt{\dfrac{P}{R}}=\sqrt{\dfrac{4.0}{20}}=0.447\,\mathrm{A}\).
The total circuit resistance is
\(R_{\text{total}}=\dfrac{V}{I}=\dfrac{16}{0.447}\approx35.8\,\Omega\).
Therefore, the variable resistance is
\(R_{\text{variable}}=35.8-20\approx15.8\,\Omega\approx16\,\Omega\).
Therefore, the correct answer is (A).
Question 38
A nucleus decays by emitting a \(\beta^{+}\) particle.
Which particle must also be emitted from the nucleus?
(B) \(\beta^{-}\) particle
(C) \(\alpha\)-particle
(D) neutrino
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
In \(\beta^{+}\) decay, a proton changes into a neutron:
\(p\rightarrow n+\beta^{+}+\nu\).
A neutrino \((\nu)\) is emitted to conserve energy, momentum and lepton number.
An antineutrino is emitted in \(\beta^{-}\) decay, not in \(\beta^{+}\) decay.
Therefore, the correct answer is (D).
Question 39
What are the charges on an antidown quark and on an antistrange quark?
| antidown quark | antistrange quark | |
|---|---|---|
| (A) | \(+\dfrac{1}{3}e\) | \(+\dfrac{1}{3}e\) |
| (B) | \(+\dfrac{1}{3}e\) | \(-\dfrac{1}{3}e\) |
| (C) | \(-\dfrac{1}{3}e\) | \(+\dfrac{1}{3}e\) |
| (D) | \(-\dfrac{1}{3}e\) | \(-\dfrac{1}{3}e\) |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
A down quark has charge
\(-\dfrac{1}{3}e\).
A strange quark also has charge
\(-\dfrac{1}{3}e\).
Antiquarks have charges equal in magnitude but opposite in sign to their corresponding quarks.
Hence, both the antidown quark and the antistrange quark have charge
\(+\dfrac{1}{3}e\).
Therefore, the correct answer is (A).
Question 40
The nucleus of a radioactive isotope of an element emits an \(\alpha\)-particle. The daughter nucleus then emits a \(\beta^{-}\) particle and then the daughter nucleus of that reaction emits another \(\beta^{-}\) particle.
Which statement describes the final nuclide that is formed?
(B) It is a nuclide of a different element of higher proton number.
(C) It is a nuclide of the same element but with different proton number.
(D) It is identical to the original nuclide.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
An \(\alpha\)-decay changes the nucleus as follows:
\(A\rightarrow A-4,\qquad Z\rightarrow Z-2\).
Each \(\beta^{-}\)-decay increases the proton number by 1 while leaving the nucleon number unchanged:
\(A=\text{constant},\qquad Z\rightarrow Z+1\).
After two \(\beta^{-}\) decays:
\(Z-2+1+1=Z\).
The final nucleus has the same proton number but a nucleon number of \(A-4\).
Hence, it is a different isotope of the original element.
Therefore, the correct answer is (A).