31 reviewed questions with answers and explanations.
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For force with dimensions MˣLʸTᶻ, what are x, y and z respectively?
B: 1, 1, −2
Force equals mass times acceleration. Mass contributes M and acceleration LT⁻², so force has dimensions M¹L¹T⁻². The exponents are 1,1,−2.
AI-reviewed · calculation checkedA particle’s position is x =10 +12 t² metres, with time t in seconds. Find its average speed from t =2 s to t =5 s.
C: 84 m/s
At 2 s, x =10 +12(2²) =58 m; at 5 s, x =310 m. Position increases throughout, so distance travelled is 252 m and average speed is 252/3 =84 m/s.
AI-reviewed · calculation checkedA 5 kg block is released on a smooth plane inclined at 30° to horizontal. Find its downslope acceleration using g =10 m/s².
A: 5.0 m/s²
The downslope component of weight is mg sin 30°. Dividing by the mass gives acceleration g sin 30° =10 ×0.5 =5.0 m/s².
AI-reviewed · calculation checkedAn arrow of mass 0.1 kg travelling horizontally at 15 m/s embeds in a stationary 0.4 kg block on a smooth horizontal surface. Find their common speed.
D: 3.0 m/s
Horizontal momentum is conserved as the arrow embeds in the block. Thus 0.1 ×15 =(0.1 +0.4)v, giving v =1.5/0.5 =3.0 m/s.
AI-reviewed · calculation checkedFor a body in simple harmonic motion, which quantities are in phase?
D: Net force and acceleration
For a fixed mass, net force F =ma. Force and acceleration therefore have the same sign and reach their extrema together. In SHM, displacement is opposite in phase to acceleration, while velocity differs by a quarter cycle.
AI-reviewed · calculation checkedThree forces act on a particle at rest: 6 N vertically downward, 6√3 N horizontally right, and 12 N upward-left along a cord. The cord makes angle θ with the vertical. Find θ.
D: 60°
Vertical equilibrium requires the upward component 12 cosθ to equal 6 N. Thus cosθ =1/2 and θ =60°. The horizontal component is 12 sin 60° =6√3 N, matching the rightward force.
AI-reviewed · calculation checkedA block of mass m slides down a rough plane inclined at θ to horizontal, with no other applied forces. Which force component and force act along the plane?
B: mg sinθ and friction
Weight resolves into mg sinθ down the slope and mg cosθ perpendicular to it. Friction acts up the slope against sliding; the normal reaction is perpendicular, so it contributes no force along the plane.
AI-reviewed · calculation checkedA 100 g object projected upward has speed 20 m/s at height 10 m. Neglect air resistance and use g =10 m/s². Find its initial kinetic energy at ground level.
C: 30 J
At 10 m height, kinetic energy is½ ×0.1 ×20² =20 J and gained potential energy is 0.1 ×10 ×10 =10 J. Initial kinetic energy is their sum,30 J.
AI-reviewed · calculation checkedA water pump draws 1.5 kW of electrical power while lifting 200 kg of water through 6 m in 10 s. Use g =10 m/s². Find its efficiency.
C: 80.0%
Useful output energy is mgh =200 ×10 ×6 =12000 J. Electrical input is 1500 ×10 =15000 J. Efficiency is 12000/15000 ×100% =80%.
AI-reviewed · calculation checkedA block of weight W rests on a rough plane inclined at θ to horizontal. When it is just about to slide under its weight, which relation holds?
A: tanθ = coefficient of static friction
At the point of slipping, downslope weight W sinθ equals limiting friction μₛW cosθ. Dividing by W cosθ gives tanθ =μₛ.
AI-reviewed · calculation checkedAn empty 60 litre tank has mass 10 kg. Find its mass when full of fuel of relative density 0.72. Use water density 1000 kg/m³.
D: 53.2 kg
The fuel volume is 60 L =0.060 m³. Its density is 0.72 ×1000 =720 kg/m³, so fuel mass is 43.2 kg. Adding the 10 kg empty tank gives 53.2 kg.
AI-reviewed · calculation checkedA mercury thermometer’s thread lengths at 0 °C, 100 °C and an unknown temperature are 25 mm, 225 mm and 175 mm respectively. Assuming linear calibration, find the unknown temperature.
C: 75.0 °C
The 100 °C interval corresponds to 225 −25 =200 mm. A 175 mm reading is 150 mm above zero, so temperature is 150/200 ×100 =75.0 °C.
AI-reviewed · calculation checkedA fixed amount of ideal gas in a tyre has absolute pressure 3 ×10⁵ Pa at 27 °C. At constant volume its absolute pressure rises to 4 ×10⁵ Pa. Find the final Celsius temperature, using K = °C +273.
D: 127 °C
At fixed volume, absolute pressure is proportional to absolute temperature. Initially T =27 +273 =300 K. The final temperature is 300 ×4/3 =400 K, or 127 °C.
AI-reviewed · calculation checkedAt ordinary atmospheric pressure, a fixed mass of pure ice melts completely to water at 0 °C. Which description is correct?
A: Latent heat is absorbed, the mass remains constant and the volume decreases.
Melting ice absorbs latent heat while conserving its mass. Ordinary ice is less dense than liquid water near 0 °C, so the same mass occupies less volume after melting.
AI-reviewed · source checkedNeglect supercooling. Which temperature-time description represents a pure molten substance cooling through complete solidification and then cooling further?
D: Temperature falls, remains constant for an interval, then falls again
A pure molten substance first cools to its freezing point. Temperature remains constant while latent heat is released during solidification, then falls again once the solid cools.
AI-reviewed · source checkedRipples on water and light waves are similar because both
B: can be refracted and diffracted
Water ripples and light can both bend when propagation conditions change and spread around edges or through openings. These are refraction and diffraction.
AI-reviewed · source checkedA plucked string’s fundamental frequency is 500 Hz at length 0.90 m. At unchanged tension and mass per unit length, what length gives fundamental frequency 150 Hz?
A: 3 m
With tension and mass per unit length fixed, the same string mode has frequency inversely proportional to length. Hence 500 ×0.90 =150 L, giving L =3 m.
AI-reviewed · calculation checkedThe colours seen in thin films of oil on the road and in soap bubbles are due to
B: Interference
Light reflected from the upper and lower film surfaces follows different optical paths. Their waves reinforce some wavelengths and cancel others, producing the visible colours.
AI-reviewed · source checkedAt a particular instant, two sinusoidal wave profiles P and Q of the same wavelength have positive crests, negative troughs and zero crossings at matching positions. When superposed at that instant, they interfere
C: constructively to produce a wave of a larger amplitude
When two wave profiles have crests, troughs and zero crossings aligned, their displacements have the same sign at each position. Adding them produces a larger amplitude: constructive interference.
AI-reviewed · calculation checkedA sonometer’s hanging load is immersed in water without touching the bucket, reducing the wire tension. With water conditions and the wire’s mass per unit length fixed, how can its original fundamental frequency be restored?
A: Decrease the vibrating length of the wire
Immersing the hanging load adds upthrust and reduces the tension in the sonometer wire. Since f =√(T/μ)/(2 L), shortening the vibrating length can offset the tension reduction and restore the original frequency.
AI-reviewed · calculation checkedLight travels at 3.0 ×10⁸ m/s in vacuum and 2.4 ×10⁸ m/s in a material. Find the material’s refractive index.
D: 1.25
Refractive index is the ratio of vacuum light speed to speed in the material: n =3.0 ×10⁸/(2.4 ×10⁸) =1.25.
AI-reviewed · calculation checkedWhich electromagnetic band is commonly used to detect temperature differences in objects near ordinary environmental temperatures?
D: Infrared
Objects near ordinary environmental temperatures emit much of their thermal radiation in the infrared. Infrared detectors can measure changes in that emission to detect temperature differences.
AI-reviewed · source checkedThree identical cells, each of emf 1.5 V and internal resistance 1 Ω, are connected in parallel with matching polarities across a 2/3 Ω resistor. Find the resistor current.
C: 1.5 A
Identical cells in parallel retain emf 1.5 V and have combined internal resistance 1/3 Ω. With the 2/3 Ω load, total resistance is 1 Ω, so current is 1.5/1 =1.5 A.
AI-reviewed · calculation checkedMoving 100 μC of charge between two points requires 8 ×10⁻² J of work. Find the magnitude of their potential difference.
C: 8.0 ×10² V
Potential difference is work per charge. Convert 100 μC to 1.00 ×10⁻⁴ C, then V =0.08/(1.00 ×10⁻⁴) =800 V.
AI-reviewed · calculation checkedIn a working metre bridge with uniform wire, resistors 2 Ω and 3 Ω occupy the left and right gaps. Find the balance position measured from the left end.
B: 40 cm
At balance, resistance ratio equals uniform-wire length ratio:2/3 =l/(100 −l). Thus 2(100 −l) =3 l, giving l =40 cm from the left.
AI-reviewed · calculation checkedTwo initially uncharged 50 μF capacitors are connected in series across a 100 V battery. Find the final charge magnitude on each capacitor plate.
B: 2.50 ×10⁻³ C
Two equal 50 μF capacitors in series have equivalent capacitance 25 μF. The series charge is 25 ×10⁻⁶ ×100 =2.50 ×10⁻³ C. Each capacitor has that charge magnitude and a 50 V drop.
AI-reviewed · calculation checkedAn electric cooker operates continuously at 1000 W for 5 hours. Find the electrical energy consumed.
C: 1.8 ×10⁷ J
Five hours is 5 ×3600 =18000 seconds. At constant 1000 W, energy used is Pt =1000 ×18000 =1.8 ×10⁷ J.
AI-reviewed · calculation checkedAn AC voltage is V =311 sin(314.2 t), with t in seconds and phase in radians. Find the frequency using π =3.142.
A: 50.0 Hz
In V =V₀ sinωt, angular frequency is 314.2 rad/s. Ordinary frequency isω/(2π) =314.2/(2 ×3.142) =50.0 Hz.
AI-reviewed · calculation checkedIn sinusoidal steady state in a purely inductive circuit, the current
A: Lags the voltage by 90°
For an ideal inductor, v =L di/dt. Differentiating a sinusoidal current advances its phase by 90°, so voltage leads current by 90° and current lags voltage by 90°.
AI-reviewed · calculation checkedA characteristic of neutron-induced uranium fission is that it can
B: Sustain a chain reaction under suitable conditions
Neutron-induced fission can release neutrons that trigger further fissions, allowing a chain reaction under suitable conditions. The released energy comes from a decrease in total rest mass.
AI-reviewed · source checkedIn a graphite-moderated uranium reactor, graphite surrounding the fuel is used mainly to
C: Slow fast neutrons to help sustain the fission chain reaction
Graphite acts as a moderator. Collisions with carbon nuclei slow fast neutrons, making them more effective at causing fission in uranium-235 and helping sustain the chain reaction.
AI-reviewed · source checked