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Chapter 6· Mechanical Properties of Matter
MCQs with Answers Try each one first: tap an option to check it, then read the reasoning and why the others are wrong.
A note about the questions
The wording follows published solved exercises and every answer was re-checked by hand, so the wording or the order of options may differ slightly from your print.
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Set A: Textbook exercise 8 MCQs The multiple-choice questions at the end of Chapter 6 in your book, in the book's option order.
Q6.1 Deformation and Elasticity
A wire is stretched by a weight w. If the diameter of the wire is reduced to half of its previous value, the extension will become:
(a) one half (b) double (c) one fourth (d) four times Show answer and reasoning Answer (d) four times
Step by step
A thinner wire stretches more: extension ∝ 1 ÷ cross-sectional area. Area = πd²/4, so halving d makes the area (½)² = ¼. Extension becomes 1 ÷ ¼ = 4 times. Why the others are wrong
(a) a thinner wire stretches more, not less.(b) that would be true only if the extension depended on d, not d².(c) ¼ is the new area, but the extension goes up by the inverse.Remember
Area goes with diameter squared.
Q6.2 Deformation and Elasticity
Four wires of the same material are stretched by the same load. Their dimensions are given below. Which of them will elongate most?
(a) length 1 m, diameter 1 mm (b) length 2 m, diameter 2 mm (c) length 3 m, diameter 3 mm (d) length 4 m, diameter 0.5 mm Show answer and reasoning Answer (d) length 4 m, diameter 0.5 mm
Step by step
For the same load and material, extension ∝ L ÷ d². (a) 1 ÷ 1² = 1; (b) 2 ÷ 2² = 0.5; (c) 3 ÷ 3² = 0.33; (d) 4 ÷ 0.5² = 16. (d) has the largest value. Why the others are wrong
(a) L ÷ d² = 1.(b) L ÷ d² = 0.5.(c) L ÷ d² = 0.33.Remember
Long and thin stretches most.
Q6.3 Pressure in Liquids
Two metal plates of area 2 and 3 square metres are placed in a liquid at the same depth. The ratio of pressures on the two plates is:
(a) 1 : 1 (b) √2 : √3 (c) 2 : 3 (d) 4 : 9 Show answer and reasoning Answer (a) 1 : 1
Step by step
P = ρgh. Same liquid and same depth, so the same pressure on both. (The force F = PA is larger on the bigger plate, but the pressure is equal.) Why the others are wrong
(b) pressure does not depend on the square root of the area.(c) 2 : 3 is the ratio of the forces, not the pressures.(d) 4 : 9 does not come from P = ρgh.Remember
Pressure, not force: area does not matter.
Q6.4 Pressure in Liquids
The pressure at any point in a liquid is proportional to:
(a) density of the liquid (b) depth of the point below the surface of the liquid (c) acceleration due to gravity (d) all of the above Show answer and reasoning Answer (d) all of the above
Step by step
P = ρgh. Doubling any one of ρ, g or h doubles the pressure. Why the others are wrong
(a) true, but not the only factor.(b) true, but not the only factor.(c) true, but not the only factor.Remember
P = ρgh: all three.
Q6.5 Pascal's Law and Hydraulics
Pressure applied to an enclosed fluid is:
(a) diminished and transmitted to the walls of the container (b) increased in proportion to the mass of the fluid and then transmitted to each part of the fluid (c) transmitted unchanged to every portion of the fluid and the walls of the containing vessel (d) applied to every part of the fluid Show answer and reasoning Answer (c) transmitted unchanged to every portion of the fluid and the walls of the containing vessel
Step by step
A liquid is almost incompressible. So a push at one place raises the pressure everywhere in it by the same amount. Why the others are wrong
(a) the pressure is not reduced.(b) the pressure is not increased by the fluid's mass.(d) vague; it leaves out that the pressure is transmitted unchanged.Remember
Pascal: unchanged, everywhere.
Q6.6 Pascal's Law and Hydraulics
The principle of a hydraulic press is based on:
(a) conservation of energy (b) Pascal's law (c) conservation of momentum (d) Archimedes' principle Show answer and reasoning Answer (b) Pascal's law
Step by step
Pressure F₁/A₁ on the small piston is transmitted unchanged to the large piston. So F₂ = F₁ × A₂/A₁, a larger force. Why the others are wrong
(a) energy is conserved, but the working principle is the transmission of pressure.(c) no collision is involved.(d) Archimedes' principle is about upthrust on floating or sunk bodies.Remember
Anything hydraulic: Pascal's law.
Q6.7 Hooke's Law
When a spring is compressed, what form of energy does it possess?
(a) kinetic (b) potential (c) internal (d) heat Show answer and reasoning Answer (b) potential
Step by step
Compressing the spring changes its shape (deformation). Energy stored by deformation is elastic potential energy. Why the others are wrong
(a) a spring held compressed is not moving.(c) the useful stored energy is elastic potential energy, not internal energy.(d) the spring stores energy; it is not heat.Remember
Squeezed or stretched spring = potential energy.
Q6.8 Atmospheric Pressure
What is the force exerted by the atmosphere on a rectangular block surface of length 50 cm and breadth 40 cm? The atmospheric pressure is 100 kPa.
(a) 20 kN (b) 100 kN (c) 200 kN (d) 500 kN Show answer and reasoning Answer (a) 20 kN
Step by step
Change cm to m: 0.5 m × 0.4 m = 0.2 m². F = P × A = 1.0 × 10⁵ × 0.2 = 2.0 × 10⁴ N. = 20 kN. Why the others are wrong
(b) 100 kN treats the area as 1 m².(c) 200 kN is ten times too large.(d) 500 kN multiplies by 5 instead of 0.2.Remember
Convert cm² to m² before multiplying.
Set B: More MCQs from this chapter 16 MCQs Extra questions on the same ideas, of the kind set in board papers and class tests.
QB1 Deformation and Elasticity
Plasticine (clay dough) that does not return to its shape after being pressed is:
(a) elastic (b) inelastic (plastic) (c) a rigid body (d) a fluid Show answer and reasoning Answer (b) inelastic (plastic)
Step by step
Elastic materials return to their shape; inelastic ones do not. Plasticine stays dented, so it is inelastic. Why the others are wrong
(a) an elastic body would return to its shape.(c) a rigid body would not change shape at all.(d) plasticine is a solid that keeps a shape.Remember
Stays dented = inelastic.
QB2 Deformation and Elasticity
If a spring is stretched beyond its elastic limit:
(a) it returns to its original length (b) it is permanently deformed (c) its spring constant doubles (d) it stops stretching Show answer and reasoning Answer (b) it is permanently deformed
Step by step
Up to the elastic limit, the spring returns to its length. Beyond it, part of the stretch stays when the load is removed. Why the others are wrong
(a) that happens only within the elastic limit.(c) the spring constant does not double.(d) it stretches even more easily and may break.Remember
Past the limit, the damage stays.
QB3 Hooke's Law
The SI unit of the spring constant k is:
(a) N m (b) N m⁻¹ (c) N m⁻² (d) kg m⁻¹ Show answer and reasoning Answer (b) N m⁻¹
Step by step
From Hooke's law, k = F ÷ x. Unit: N ÷ m = N m⁻¹. Why the others are wrong
(a) N m is the unit of work or torque.(c) N m⁻² is the pascal, the unit of pressure.(d) kg m⁻¹ has no force in it.Remember
Force per metre of stretch.
QB4 Hooke's Law
A spring of spring constant 200 N m⁻¹ is stretched by 0.05 m. The force applied is:
(a) 10 N (b) 4000 N (c) 40 N (d) 0.25 N Show answer and reasoning Answer (a) 10 N
Step by step
Hooke's law: F = kx. F = 200 × 0.05 = 10 N. Why the others are wrong
(b) 4000 divides by 0.05 instead of multiplying.(c) 40 N does not come from kx.(d) 0.25 divides x by k.Remember
F = kx, with x in metres.
QB5 Hooke's Law
Within the elastic limit, a graph of force against extension for a spring is:
(a) a straight line through the origin (b) a curve rising steeply (c) a horizontal line (d) a vertical line Show answer and reasoning Answer (a) a straight line through the origin
Step by step
Direct proportion gives a straight line through (0, 0). The slope F ÷ x is the spring constant k. Why the others are wrong
(b) the graph only curves beyond the elastic limit.(c) that would mean the force does not change.(d) that would mean no extension at all.Remember
Proportional = straight line through zero.
QB6 Hooke's Law
Two identical springs, each of spring constant k, are joined end to end (in series). The spring constant of the combination is:
Show answer and reasoning Answer (c) k/2
Step by step
A load L stretches one spring by x, so k = L ÷ x. In series both springs carry L, so the total extension is x + x = 2x. New k = L ÷ 2x = k/2. Why the others are wrong
(a) 2k is for two springs side by side (parallel).(b) the combination stretches twice as much.(d) 4k does not come from either arrangement.Remember
Series: softer (k/2). Parallel: stiffer (2k).
QB7 Density
The SI unit of density is:
(a) g cm⁻³ (b) kg m⁻³ (c) kg m⁻² (d) N m⁻³ Show answer and reasoning Answer (b) kg m⁻³
Step by step
ρ = m ÷ V. SI unit: kg ÷ m³ = kg m⁻³. Why the others are wrong
(a) g cm⁻³ is also used, but it is not the SI unit.(c) kg m⁻² is mass per area.(d) N m⁻³ is weight per volume.Remember
Mass per volume: kg per m³.
QB8 Density
1 g cm⁻³ is equal to:
(a) 1 kg m⁻³ (b) 10 kg m⁻³ (c) 1000 kg m⁻³ (d) 100 kg m⁻³ Show answer and reasoning Answer (c) 1000 kg m⁻³
Step by step
1 g = 10⁻³ kg. 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³. 10⁻³ ÷ 10⁻⁶ = 10³ = 1000 kg m⁻³. Why the others are wrong
(a) it forgets the different sizes of g and kg, cm³ and m³.(b) 10 does not come from the conversion.(d) 100 uses cm² instead of cm³.Remember
Water: 1 g cm⁻³ = 1000 kg m⁻³.
QB9 Density
The density of mercury is about:
(a) 1.0 × 10³ kg m⁻³ (b) 7.8 × 10³ kg m⁻³ (c) 2.7 × 10³ kg m⁻³ (d) 13.6 × 10³ kg m⁻³ Show answer and reasoning Answer (d) 13.6 × 10³ kg m⁻³
Step by step
Water: 1000 kg m⁻³. Mercury: 13.6 × 1000 = 13 600 kg m⁻³. Why the others are wrong
(a) that is water.(b) that is iron.(c) that is aluminium.QB10 Pressure
One pascal is equal to:
(a) 1 N m⁻² (b) 1 N m (c) 1 N m² (d) 1 N s Show answer and reasoning Answer (a) 1 N m⁻²
Step by step
P = F ÷ A. 1 Pa = 1 N m⁻². Why the others are wrong
(b) N m is the joule.(c) it multiplies by area instead of dividing.(d) N s is impulse.Remember
Newton per square metre.
QB11 Pressure
A sharp knife cuts better than a blunt one because:
(a) it applies a larger force (b) it is heavier (c) its small edge area gives a large pressure (d) it has less friction Show answer and reasoning Answer (c) its small edge area gives a large pressure
Step by step
P = F ÷ A. Sharp edge: very small A, so large P for the same push. Why the others are wrong
(a) you push with the same force.(b) sharpening does not make the knife heavier.(d) friction is not the reason.Remember
Small area, big pressure.
QB12 Atmospheric Pressure
Standard atmospheric pressure at sea level is about:
(a) 1.013 × 10⁵ Pa (b) 1.013 × 10³ Pa (c) 760 Pa (d) 10⁵ N Show answer and reasoning Answer (a) 1.013 × 10⁵ Pa
Step by step
P = ρgh = 13 600 × 9.8 × 0.76 ≈ 1.013 × 10⁵ Pa. Why the others are wrong
(b) a hundred times too small.(c) 760 is in millimetres of mercury, not pascals.(d) newton is a unit of force, not pressure.Remember
About 100 000 Pa = 100 kPa = 760 mm of mercury.
QB13 Atmospheric Pressure
As we go higher above sea level, atmospheric pressure:
(a) increases (b) stays the same (c) decreases (d) becomes zero straight away Show answer and reasoning Answer (c) decreases
Step by step
Atmospheric pressure comes from the air above. Going up leaves less air above, so the pressure falls. Why the others are wrong
(a) it is the other way round.(b) it changes with height (that is how altimeters work).(d) it falls gradually, not suddenly.Remember
Higher = less air above = lower pressure.
QB14 Pressure in Liquids
The pressure due to water at a depth of 5 m (density 1000 kg m⁻³, g = 10 m s⁻²) is:
(a) 5000 Pa (b) 500 Pa (c) 50 000 Pa (d) 5 × 10⁶ Pa Show answer and reasoning Answer (c) 50 000 Pa
Step by step
P = ρgh. 1000 × 10 × 5 = 5 × 10⁴ Pa. Why the others are wrong
(a) it leaves out g.(b) far too small.(d) a hundred times too large.Remember
Every 10 m of water adds about 10⁵ Pa.
QB15 Pressure in Liquids
The walls of a dam are made thicker at the bottom because:
(a) it makes the dam look strong (b) water is lighter at the bottom (c) pressure decreases with depth (d) pressure increases with depth Show answer and reasoning Answer (d) pressure increases with depth
Step by step
Liquid pressure grows with depth. The deepest part of the wall feels the biggest pressure, so it is made thickest. Why the others are wrong
(a) the shape is for strength, not looks.(b) water has the same density at the bottom.(c) it is the other way round.Remember
Deeper = more pressure.
QB16 Pascal's Law and Hydraulics
In a hydraulic jack the small piston has an area of 0.01 m² and the large piston 0.5 m². A force of 100 N on the small piston can support a load of:
(a) 2 N (b) 50 N (c) 500 N (d) 5000 N Show answer and reasoning Answer (d) 5000 N
Step by step
Pascal's law: F₁ ÷ A₁ = F₂ ÷ A₂. F₂ = 100 × 0.5 ÷ 0.01 = 100 × 50 = 5000 N. Why the others are wrong
(a) 2 N divides by the area ratio instead of multiplying.(b) 50 is the area ratio, not the force.(c) 500 N is ten times too small.Remember
Force is multiplied by the area ratio.
