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Question 1Matter
Which state of matter has a definite volume but no fixed shape?
- Plasma
- Gas
- Solid
- Liquid Correct answer.
Explanation
In a liquid the molecules are close together but free to slide past one another, so the volume is fixed while the shape adapts to the container. Solids keep both a fixed volume and a fixed shape, and gases fill whatever space is available.
Question 2Matter
The SI unit of density is:
- g/cm³
- kg·m³
- kg/m³ Correct answer.
- N/m³
Explanation
Density is mass divided by volume, so in SI base units it is expressed in kilograms per cubic metre. Units such as g/cm³ belong to the CGS system, and N/m³ describes weight per unit volume rather than mass per unit volume.
Question 3Matter
The irregular, jittery motion of smoke particles suspended in air is best explained as evidence of:
- the random motion of air molecules Correct answer.
- surface tension acting on the particles
- convection currents in the container
- electrostatic repulsion between particles
Explanation
Smoke particles are struck unevenly and at random by fast-moving air molecules, so they follow a zig-zag path known as Brownian motion. This behaviour supports the kinetic model, in which the molecules of a fluid are themselves in continuous random motion.
Question 4Matter
One pascal is equal to:
- 1 N/m² Correct answer.
- 1 kg/m³
- 1 N·m
- 1 J/s
Explanation
Pressure is force divided by area, so one pascal is one newton acting over one square metre. It measures pressure only and is not a unit of energy, power or density.
Question 5Matter
Hooke's law states that, below the limit of proportionality, the extension of an elastic body is directly proportional to:
- the cross-sectional area
- the original length
- the square of the applied load
- the applied load Correct answer.
Explanation
Hooke's law relates the deformation of an elastic body to the force causing it: doubling the load doubles the extension, provided the limit of proportionality is not exceeded. The constant of proportionality is the stiffness of the particular specimen.
Question 6Matter
The relative density of a substance is the ratio of its density to the density of:
- pure water at 4 °C Correct answer.
- air at sea level
- mercury at 0 °C
- the same substance as a gas
Explanation
Relative density, or specific gravity, compares a substance with pure water at 4 °C, whose density is taken as 1000 kg/m³. Because it is a ratio of two densities it has no units.
Question 7Matter
A block has a volume of 0.002 m³ and a mass of 5.4 kg. Its density is:
- 10 800 kg/m³
- 2700 kg/m³ Correct answer.
- 270 kg/m³
- 108 kg/m³
Explanation
Density is mass divided by volume, so 5.4 kg ÷ 0.002 m³ = 2700 kg/m³. This is typical of a light metal such as aluminium.
Question 8Matter
Taking g = 10 m/s², the pressure due to a column of liquid of density 1000 kg/m³ at a depth of 5 m is:
- 500 kPa
- 50 kPa Correct answer.
- 500 Pa
- 5 kPa
Explanation
The pressure due to a liquid column is p = ρgh = 1000 × 10 × 5 = 50 000 Pa, which is 50 kPa. The shape or width of the containing vessel does not affect this result.
Question 9Matter
A bimetallic strip bends when heated because the two metals have different:
- thermal conductivities
- coefficients of linear expansion Correct answer.
- mass densities
- specific heat capacities
Explanation
Both metals are heated through the same temperature rise, but the one with the greater coefficient of linear expansion lengthens more, so the strip curves towards the metal that expands less. This effect is used in thermostats and in some thermometers.
Question 10Matter
A fixed mass of gas occupies 2 m³ at 100 kPa. If it is compressed to 0.5 m³ at constant temperature, its new pressure is:
- 400 kPa Correct answer.
- 25 kPa
- 800 kPa
- 100 kPa
Explanation
Boyle's law states that for a fixed mass of gas at constant temperature, pV is constant. Thus 100 kPa × 2 m³ = p₂ × 0.5 m³, giving p₂ = 400 kPa.
Question 11Matter
Which statement about viscosity is correct?
- The viscosity of a liquid rises as its temperature rises.
- The viscosity of a liquid falls as its temperature rises. Correct answer.
- Viscosity is independent of temperature for both liquids and gases.
- The viscosity of a gas falls as its temperature rises.
Explanation
In a liquid, heating gives the molecules enough energy to slide past each other more readily, so viscosity decreases. In a gas the opposite happens, because faster molecules exchange momentum between layers more effectively.
Question 12Matter
A wire 2 m long and of cross-sectional area 1 × 10⁻⁶ m² extends by 1 mm under a load of 100 N. The Young's modulus of the material is:
- 2 × 10⁸ Pa
- 2 × 10¹¹ Pa Correct answer.
- 5 × 10¹⁰ Pa
- 1 × 10¹¹ Pa
Explanation
Stress = force/area = 100 ÷ 1 × 10⁻⁶ = 1 × 10⁸ Pa, and strain = extension/original length = 1 × 10⁻³ ÷ 2 = 5 × 10⁻⁴. Young's modulus is stress divided by strain, giving 2 × 10¹¹ Pa.
Question 13Matter
Water rises to a height h in a clean glass capillary tube. If a tube of half the internal radius is used with the same liquid, the water rises to:
- half the height
- twice the height Correct answer.
- four times the height
- the same height
Explanation
Capillary rise is given by h = 2T cos θ / (ρgr), so the height is inversely proportional to the bore radius. Halving the radius therefore doubles the height for the same liquid and tube material.
Question 14Matter
A spring extends by 30 mm when a load of 6 N is hung on it, within its elastic limit. The extension produced by a load of 10 N is:
- 30 mm
- 18 mm
- 50 mm Correct answer.
- 60 mm
Explanation
Within the elastic limit the extension is proportional to the load, giving a spring constant of 6 N ÷ 30 mm = 0.2 N/mm. A 10 N load therefore produces 10 ÷ 0.2 = 50 mm of extension.
Question 15Matter
The pressure exerted by a gas on the walls of its container is caused by:
- chemical reaction with the walls
- the attraction between molecules
- the weight of the gas molecules
- molecular impacts on the walls Correct answer.
Explanation
Gas pressure arises from countless molecular collisions with the container walls. Each impact changes the molecule's momentum, and the rate of change of momentum per unit area is the pressure exerted on the wall.
Question 16Matter
A fixed mass of gas occupies 3 m³ at 27 °C and constant pressure. When heated to 327 °C its volume becomes:
- 12 m³
- 1.5 m³
- 3.3 m³
- 6 m³ Correct answer.
Explanation
Charles's law states that V/T is constant at constant pressure, with temperature measured in kelvin. The temperature doubles from 300 K to 600 K, so the volume doubles to 6 m³.
Question 17Matter
A solid block floats in water with 40 % of its volume above the surface. The density of the block is:
- 1000 kg/m³
- 400 kg/m³
- 667 kg/m³
- 600 kg/m³ Correct answer.
Explanation
A floating body displaces its own weight of liquid, so the submerged fraction of its volume equals the ratio of its density to that of the liquid. With 60 % submerged, the density is 0.60 × 1000 = 600 kg/m³.
Question 18Matter
2 litres of a liquid of density 800 kg/m³ are mixed with 3 litres of a liquid of density 1200 kg/m³, with no change in total volume. The density of the mixture is:
- 1100 kg/m³
- 1000 kg/m³
- 1040 kg/m³ Correct answer.
- 960 kg/m³
Explanation
The masses are 2 × 10⁻³ m³ × 800 = 1.6 kg and 3 × 10⁻³ m³ × 1200 = 3.6 kg, a total of 5.2 kg. Dividing by the total volume of 5 × 10⁻³ m³ gives 1040 kg/m³.
Question 19Matter
A wire of length L and cross-sectional area A extends by e under a load F. A second wire of the same material has twice the length and twice the cross-sectional area. Under the same load it extends by:
- e/2
- 4e
- 2e
- e Correct answer.
Explanation
The extension is e = FL/(AE), so it depends on the ratio of length to area. Doubling both L and A leaves that ratio unchanged, so the extension is the same as before.
Question 20Matter
A sphere of volume 4 × 10⁻⁴ m³ and density 2500 kg/m³ is suspended from a spring balance and fully immersed in a liquid of density 900 kg/m³. Taking g = 10 m/s², the balance reads:
- 3.6 N
- 6.4 N Correct answer.
- 13.6 N
- 10.0 N
Explanation
The weight is ρVg = 2500 × 4 × 10⁻⁴ × 10 = 10 N, and the upthrust is 900 × 4 × 10⁻⁴ × 10 = 3.6 N. The balance supports the difference, so it reads 6.4 N.
Question 21Mechanics (statics, kinematics, dynamics, fluid dynamics)
A body has zero resultant force acting on it. Which statement describes its motion?
- It slows down gradually until it stops.
- It keeps a constant velocity. Correct answer.
- It moves in a circle at a constant speed.
- It accelerates in the direction of the largest force.
Explanation
Newton's first law states that a body continues at rest or in uniform motion in a straight line unless a resultant force acts on it. Zero resultant force therefore means zero acceleration, so the velocity is unchanged in both magnitude and direction.
Question 22Mechanics (statics, kinematics, dynamics, fluid dynamics)
Which of the following is the SI unit of force?
- newton Correct answer.
- joule
- watt
- pascal
Explanation
The newton is defined as the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². The joule, pascal and watt are units of energy, pressure and power respectively.
Question 23Mechanics (statics, kinematics, dynamics, fluid dynamics)
A vehicle travels 150 m in 10 s at a steady rate. Its average speed is:
- 0.67 m/s
- 1.5 m/s
- 15 m/s Correct answer.
- 150 m/s
Explanation
Average speed is the distance travelled divided by the time taken, so 150 m ÷ 10 s = 15 m/s. This is a scalar quantity and carries no direction information.
Question 24Mechanics (statics, kinematics, dynamics, fluid dynamics)
A metal block has a mass of 540 g and a volume of 60 cm³. Its density is:
- 0.11 g/cm³
- 32 400 g/cm³
- 9 g/cm³ Correct answer.
- 600 g/cm³
Explanation
Density is mass divided by volume, so 540 g ÷ 60 cm³ = 9 g/cm³, which equals 9000 kg/m³. The result shows the material is denser than water.
Question 25Mechanics (statics, kinematics, dynamics, fluid dynamics)
Which of the following quantities is a vector?
- Velocity Correct answer.
- Energy
- Mass
- Temperature
Explanation
A vector needs both magnitude and direction for its complete description. Velocity has direction as well as size, whereas mass, temperature and energy are scalars described by magnitude alone.
Question 26Mechanics (statics, kinematics, dynamics, fluid dynamics)
An object of mass 25 kg is taken to a place where the acceleration due to gravity is 9.8 m/s². Its weight there is:
- 2.55 N
- 25 N
- 0.39 N
- 245 N Correct answer.
Explanation
Weight is the gravitational force on a mass, given by W = mg. Substituting gives 25 kg × 9.8 m/s² = 245 N, and weight is a force measured in newtons.
Question 27Mechanics (statics, kinematics, dynamics, fluid dynamics)
A force of 200 N acts normally on an area of 0.5 m². The pressure produced is:
- 0.0025 Pa
- 100 Pa
- 4 Pa
- 400 Pa Correct answer.
Explanation
Pressure is the normal force divided by the area over which it acts, p = F/A. Here 200 N ÷ 0.5 m² = 400 Pa, and a smaller area would give a larger pressure.
Question 28Mechanics (statics, kinematics, dynamics, fluid dynamics)
A spring extends by 4 cm when a force of 8 N is applied to it. Its spring constant is:
- 32 N/m
- 2 N/m
- 200 N/m Correct answer.
- 0.5 N/m
Explanation
Hooke's law gives F = kx, so the spring constant is k = F/x. Converting 4 cm to 0.04 m gives 8 N ÷ 0.04 m = 200 N/m.
Question 29Mechanics (statics, kinematics, dynamics, fluid dynamics)
A stone is released from rest and falls freely for 3 s. Taking g = 9.8 m/s², its speed just before impact is about:
- 29.4 m/s Correct answer.
- 44.1 m/s
- 9.8 m/s
- 88.2 m/s
Explanation
For motion from rest under constant acceleration, v = gt. Thus v = 9.8 m/s² × 3 s = 29.4 m/s, and the speed grows linearly with time.
Question 30Mechanics (statics, kinematics, dynamics, fluid dynamics)
A beam is pivoted at its centre. A 60 N force acts 2 m from the pivot on one side. On the other side, a force 3 m from the pivot keeps the beam in equilibrium. The magnitude of this force is:
- 40 N Correct answer.
- 20 N
- 120 N
- 90 N
Explanation
For rotational equilibrium the clockwise moments must equal the anticlockwise moments. Here 60 N × 2 m = F × 3 m, so F = 40 N.
Question 31Mechanics (statics, kinematics, dynamics, fluid dynamics)
A 1200 kg aircraft has a forward thrust of 30 kN and a total drag of 6 kN. Its horizontal acceleration is:
- 20 m/s² Correct answer.
- 0.05 m/s²
- 25 m/s²
- 5 m/s²
Explanation
The resultant force is the thrust minus the drag, 30 kN − 6 kN = 24 kN. Newton's second law then gives a = F/m = 24 000 N ÷ 1200 kg = 20 m/s².
Question 32Mechanics (statics, kinematics, dynamics, fluid dynamics)
A 2 kg trolley moving at 3 m/s collides with a stationary 4 kg trolley and the two move off together. Their common velocity is:
- 1 m/s Correct answer.
- 1.5 m/s
- 0.67 m/s
- 3 m/s
Explanation
Total momentum is conserved in the collision: 2 kg × 3 m/s = 6 kg·m/s before, and (2 + 4) kg × v after. Solving gives v = 1 m/s.
Question 33Mechanics (statics, kinematics, dynamics, fluid dynamics)
A wooden block floats in water with exactly half of its volume of 0.02 m³ submerged. Taking the density of water as 1000 kg/m³ and g as 9.8 m/s², the upthrust on the block is:
- 196 N
- 49 N
- 20 N
- 98 N Correct answer.
Explanation
Archimedes' principle gives upthrust equal to the weight of fluid displaced. The displaced volume is 0.01 m³, so the upthrust is 1000 × 9.8 × 0.01 = 98 N.
Question 34Mechanics (statics, kinematics, dynamics, fluid dynamics)
Water flows at 3 m/s through a pipe section of cross-sectional area 0.02 m² and then enters a section of area 0.06 m². The speed in the wider section is:
- 0.33 m/s
- 1 m/s Correct answer.
- 9 m/s
- 3 m/s
Explanation
For an incompressible fluid the continuity equation gives A₁v₁ = A₂v₂. Since the area triples, the speed falls to one third: 0.02 × 3 = 0.06 × v, so v = 1 m/s.
Question 35Mechanics (statics, kinematics, dynamics, fluid dynamics)
In a horizontal pipe carrying a steady flow, the fluid speeds up at a constriction. The static pressure at the constriction:
- decreases Correct answer.
- increases
- remains constant
- becomes zero
Explanation
Bernoulli's equation shows that for steady horizontal flow the sum of static and dynamic pressure is constant. Where the speed rises, the dynamic pressure rises and the static pressure must fall.
Question 36Mechanics (statics, kinematics, dynamics, fluid dynamics)
A block of weight 500 N rests on a smooth plane inclined at 30° to the horizontal. The component of its weight acting down the slope is:
- 433 N
- 250 N Correct answer.
- 500 N
- 125 N
Explanation
The weight resolves into a component down the slope, W sin θ, and one perpendicular to it, W cos θ. Thus the down-slope component is 500 N × sin 30° = 250 N.
Question 37Mechanics (statics, kinematics, dynamics, fluid dynamics)
A body moves at a constant speed of 8 m/s around a circle of radius 4 m. Its centripetal acceleration is:
- 32 m/s²
- 16 m/s² Correct answer.
- 64 m/s²
- 2 m/s²
Explanation
Centripetal acceleration is given by a = v²/r. Substituting gives 8² ÷ 4 = 16 m/s², directed towards the centre of the circle.
Question 38Mechanics (statics, kinematics, dynamics, fluid dynamics)
The kinetic energy of a 4 kg mass moving at 5 m/s is:
- 20 J
- 50 J Correct answer.
- 100 J
- 10 J
Explanation
Kinetic energy is given by E = ½mv². Substituting gives 0.5 × 4 × 25 = 50 J, and the energy scales with the square of the speed.
Question 39Mechanics (statics, kinematics, dynamics, fluid dynamics)
A parachutist falls at a steady terminal velocity. At that moment the parachutist has:
- zero weight
- maximum acceleration
- a net downward force
- zero resultant force Correct answer.
Explanation
Terminal velocity is reached when the upward drag equals the downward weight, so the resultant force becomes zero. With no resultant force the acceleration is zero and the velocity stays constant.
Question 40Mechanics (statics, kinematics, dynamics, fluid dynamics)
The gauge pressure due to a column of liquid of height h and density ρ is given by:
- ρh/g
- ρgh Correct answer.
- ρg/h
- h/(ρg)
Explanation
The pressure at the base of a column equals the weight of the column per unit area, giving p = ρgh. The result increases with both the depth and the density of the liquid.
Question 41Mechanics (statics, kinematics, dynamics, fluid dynamics)
A car accelerates uniformly from rest to 20 m/s in 8 s, then brakes uniformly to rest in 4 s. The total distance travelled is:
- 80 m
- 240 m
- 120 m Correct answer.
- 160 m
Explanation
For uniform acceleration the distance is the average speed multiplied by the time. The first stage covers 10 m/s × 8 s = 80 m and the second covers 10 m/s × 4 s = 40 m, giving 120 m in total.
Question 42Mechanics (statics, kinematics, dynamics, fluid dynamics)
Water flows horizontally through a pipe. At section A the area is 0.01 m², the speed is 2 m/s and the pressure is 200 kPa. At section B the area is 0.005 m². Taking the density of water as 1000 kg/m³, the pressure at B is:
- 188 kPa
- 206 kPa
- 194 kPa Correct answer.
- 200 kPa
Explanation
Continuity gives v_B = (0.01 × 2)/0.005 = 4 m/s. Bernoulli then gives p_B = 200 000 + ½ × 1000 × (2² − 4²) = 200 000 − 6000 = 194 kPa.
Question 43Mechanics (statics, kinematics, dynamics, fluid dynamics)
A force of 50 N is applied to a spanner at 0.2 m from a nut, at 30° to the handle. The moment about the nut is:
- 10 N·m
- 0.5 N·m
- 5 N·m Correct answer.
- 8.7 N·m
Explanation
Only the component of force perpendicular to the handle produces a moment, so M = Fd sin θ. Here 50 × 0.2 × sin 30° = 5 N·m.
Question 44Mechanics (statics, kinematics, dynamics, fluid dynamics)
In a hydraulic press a force of 100 N is applied to a piston of area 0.005 m². The output piston has an area of 0.2 m². The force it can exert is:
- 2.5 N
- 400 N
- 4000 N Correct answer.
- 2500 N
Explanation
Pascal's principle gives equal pressure throughout the fluid, so F₁/A₁ = F₂/A₂. The pressure is 100/0.005 = 20 000 Pa, and F₂ = 20 000 × 0.2 = 4000 N.
Question 45Mechanics (statics, kinematics, dynamics, fluid dynamics)
A ball of mass 0.2 kg strikes a wall horizontally at 10 m/s and rebounds along the same line at 8 m/s. The magnitude of its change in momentum is:
- 1.8 kg·m/s
- 0.4 kg·m/s
- 3.6 kg·m/s Correct answer.
- 2.0 kg·m/s
Explanation
Momentum is a vector, so the reversal of direction must be included: Δp = m(v₂ − v₁) = 0.2 × (−8 − 10) = −3.6 kg·m/s. The magnitude is 3.6 kg·m/s, and the impulse from the wall is equal to this change.
Question 46Mechanics (statics, kinematics, dynamics, fluid dynamics)
Which of the following is a vector quantity?
- Temperature
- Energy
- Displacement Correct answer.
- Mass
Explanation
A vector quantity has both magnitude and direction and must be combined by vector addition. Displacement, velocity, acceleration and force are vectors, while mass, temperature, energy and speed are scalars.
Question 47Mechanics (statics, kinematics, dynamics, fluid dynamics)
A block of material has a mass of 300 g and a volume of 120 cm³. Its density is:
- 2500 kg/m³ Correct answer.
- 250 kg/m³
- 0.4 kg/m³
- 400 kg/m³
Explanation
Density is mass divided by volume, so 300/120 = 2.5 g/cm³. Since 1 g/cm³ equals 1000 kg/m³, the density is 2500 kg/m³.
Question 48Mechanics (statics, kinematics, dynamics, fluid dynamics)
A mass of 5 kg is raised vertically through a height of 12 m. Taking g = 9.8 m/s², the gain in gravitational potential energy is:
- 4.9 kJ
- 60 J
- 588 J Correct answer.
- 49 J
Explanation
The gain in gravitational potential energy is given by mgh. Substituting gives 5 × 9.8 × 12 = 588 J.
Question 49Mechanics (statics, kinematics, dynamics, fluid dynamics)
The forward motion of a rocket in space is explained by:
- the gradual decrease in the mass of the rocket
- the reaction to the exhaust gases ejected backwards Correct answer.
- the rocket pushing steadily against the surrounding air
- Newton's first law of motion
Explanation
Newton's third law states that to every action there is an equal and opposite reaction. The rocket expels gas backwards and the gas exerts an equal forward force on the rocket, so no surrounding medium is needed.
Question 50Mechanics (statics, kinematics, dynamics, fluid dynamics)
Two parallel forces of 30 N each, acting in opposite directions, form a couple. The perpendicular distance between their lines of action is 0.4 m. The moment of the couple is:
- 120 N·m
- 75 N·m
- 6 N·m
- 12 N·m Correct answer.
Explanation
The moment of a couple equals one of the forces multiplied by the perpendicular distance between them. Here 30 × 0.4 = 12 N·m, and this value is the same about any point.