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CBSE · Class 11 · Physics

Mechanical Properties of Solids

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
A load of 2100 N hangs from a wire of cross-section 2 mm2. The stress in the wire is:
  1. 1,050 × 106 N/m2
  2. 1,050 × 103 N/m2
  3. 4,200 × 106 N/m2
  4. 1,050 N/m2
2.
A glass wire 8 m long, of cross-section 25 mm2, carries a load of 3600 N. Its extension is (Y = 65 × 109 N/m2):
  1. 35.45 mm
  2. 1.77 mm
  3. 17.72 mm
  4. 177.23 mm
3.
A wire 2 m long and 25 mm2 in cross-section stretches by 0.76 mm under a load of 1900 N. Its Young's modulus is:
  1. 2000 × 109 N/m2
  2. 200 × 106 N/m2
  3. 20 × 109 N/m2
  4. 200 × 109 N/m2
4.
A pressure of 21 × 106 N/m2 acts on aluminium (bulk modulus 72 × 109 N/m2). The fractional decrease in its volume is:
  1. 2.92 × 10−4
  2. 2.92 × 10−5
  3. 0.292
  4. 0.00292
5.
Hooke's law says that, within the elastic limit, stress is proportional to:
  1. strain
  2. the square of strain
  3. density
  4. temperature
6.
A wire 5 m long stretches by 3 mm. The strain is:
  1. 1.67
  2. 0.6
  3. 0.0006
  4. 0.006
7.
Two wires of the same material carry the same load. Wire A has length 2L and diameter 3d; wire B has length 3L and diameter 2d. The ratio of their extensions A : B is:
  1. 2 : 3
  2. 27 : 8
  3. 4 : 9
  4. 8 : 27
8.
Assertion (A): If a wire carrying 3000 N is replaced by one of the same material with twice the cross-section, the stress becomes twice as large.
Reason (R): Stress is the force per unit cross-sectional area.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
A glass wire 8 m long with cross-section 2 mm2 supports 3600 N. Find the stress, the strain and the extension. (Y = 65 × 109 N/m2)
10.
In an experiment, a wire 10 m long with cross-section 25 mm2 stretches 18.86 mm when 3300 N is hung on it. Find Young's modulus. Which metal could it be?
11.
9 litres of steel is put under an extra pressure of 34 × 106 N/m2. Find the decrease in its volume. (Bulk modulus = 160 × 109 N/m2)
12.
A iron block has a face of area 500 mm2. A shearing force of 37,000 N acts on it. Find the shear strain (angle of shear, in radians). (Shear modulus = 70 × 109 N/m2)
13.
A wire stretches by 10.46 mm under a load of 3400 N. Find the elastic potential energy stored in it.
14.
A iron wire and a steel wire, each 1 m long with cross-section 10 mm2, are joined end to end and carry a load of 1700 N. Find the extension of each and the total. (Y: iron 190 GPa, steel 200 GPa)
15.
The breaking stress of a metal is 500 × 106 N/m2. What is the greatest load a wire of cross-section 10 mm2 can hold? What mass is that? (Take g = 10 m/s2.)
16.
Find the compressibility of glass, whose bulk modulus is 37 × 109 N/m2, and the percentage decrease in its volume under an extra pressure of 155 × 106 N/m2.
Section C — Word problems4 × 4 = 16 marks
17.
Two wires, one iron (Y = 190 GPa) and one steel (Y = 200 GPa), have the same length 4 m and cross-section 10 mm2. Each carries 1500 N. (a) Find the stress in each. (b) Find the extensions and their ratio. (c) Which material is more elastic?
18.
A wire 4 m long, cross-section 4 mm2, gives these extensions: 300 N → 2.5 mm; 600 N → 5 mm; 900 N → 7.5 mm; 1200 N → 10 mm. (a) Show that the extension is proportional to the load. (b) Find Young's modulus. (c) Which material is it?
19.
A iron ball is taken to a depth of 700 m in the sea. (a) What is the extra pressure on it? (b) What is the fractional decrease in its volume? (Bulk modulus 100 × 109 N/m2; density of water 1000 kg/m3; g = 10 m/s2.)
20.
A aluminium wire (Y = 70 × 109 N/m2) 5 m long, cross-section 8 mm2, carries 1300 N. Find (a) the stress, (b) the strain, (c) the energy stored per unit volume, (d) the total energy stored.
AmbifulWorksheets
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CBSE · Class 11 · Physics

Answer key

Mechanical Properties of Solids · AW-11P-MPS-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(a) 1,050 × 106 N/m2stress = F/A = 2100 ÷ (2 × 10−6)
2(c) 17.72 mmΔL = FL/(AY); with A in mm2 and Y in GPa, ΔL comes out in mm
3(d) 200 × 109 N/m2Y = FL/(AΔL)
4(a) 2.92 × 10−4ΔV/V = p/B
5(a) strain—
6(c) 0.0006strain = ΔL/L = 3 × 10−3 ÷ 5
7(d) 8 : 27ΔL ∝ L/d2
8(d) A is false, but R is true.A is false: stress = F/A, so doubling A halves the stress. R is true.
9Stress 1,800 × 106 N/m2; strain 0.0277; extension 221.54 mmstrain = stress/Y; ΔL = strain × L
1070 × 109 N/m2; aluminiumY = FL/(AΔL)
110.00191 litres (= 1.91 cm3)ΔV = pV/B
120.00106 radθ = F/(AG)
1317.78 JU = ½FΔL = ½ × 3400 × 10.46 × 10−3
14iron: 0.89 mm; steel: 0.85 mm; total 1.74 mmthe same tension acts in both wires
155,000 N; 500 kgload = breaking stress × area
162.70 × 10−11 m2/N; 0.419%compressibility = 1/B; ΔV/V = p/B
17(a) Both 150 × 106 N/m2. (b) 3.16 mm and 3 mm, ratio 20 : 19. (c) steel, which has the larger Young's modulus (less strain for the same stress).—
18(a) Load ÷ extension = 120 N/mm each time, so they are proportional (Hooke's law). (b) 120 × 109 N/m2. (c) copper.Y = (F/ΔL) × L/A
19(a) 7.00 × 106 N/m2; (b) 7.00 × 10−5p = ρgh; ΔV/V = p/B
20(a) 162.5 × 106 N/m2; (b) 0.00232; (c) 1.89 × 105 J/m3; (d) 7.54 Ju = ½ × stress × strain; volume = AL