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Chapter 9: Mechanical Properties of Solids

NCERT Solutions for CBSE Class 10 Physics — 104 solved questions with detailed explanations.

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Solved Questions

Q1. Young's modulus is defined as the ratio of:

Stress to strain
Strain to stress
Force to area
Extension to length

Difficulty: Easy · Topic: Young's Modulus

Solution

Young's modulus Y = Longitudinal stress / Longitudinal strain = (F/A) / (ΔL/L).

Q2. Poisson's ratio is the ratio of:

Longitudinal strain to lateral strain
Lateral strain to longitudinal strain
Stress to strain
Shearing stress to shearing strain

Difficulty: Easy · Topic: Poisson's Ratio

Solution

Poisson's ratio σ = Lateral strain / Longitudinal strain.

Q3. The bulk modulus of a material is the ratio of:

Volume stress to volume strain
Shearing stress to shearing strain
Longitudinal stress to longitudinal strain
Tensile stress to compressive strain

Difficulty: Easy · Topic: Bulk Modulus

Solution

Bulk modulus B = Volume stress (pressure change) / Volume strain (ΔV/V).

Q4. Bulk modulus is defined as the ratio of:

lateral strain to longitudinal strain
longitudinal stress to longitudinal strain
volume stress to volume strain
shearing stress to shearing strain

Difficulty: Easy · Topic: Elastic Moduli

Solution

Bulk modulus = volume stress to volume strain.

Q5. Shear modulus (Rigidity) is defined as the ratio of:

lateral strain to longitudinal strain
shearing stress to shearing strain
volume stress to volume strain
longitudinal stress to longitudinal strain

Difficulty: Easy · Topic: Elastic Moduli

Solution

Shear modulus (Rigidity) = shearing stress to shearing strain.

Q6. A wire of length 2 m and cross-sectional area 2 mm² is stretched by 1 mm under a force of 400 N. Young's modulus is:

2 × 10¹ N/m²
4 × 10¹ N/m²
4 × 10¹¹ N/m²
2 × 10¹¹ N/m²

Difficulty: Medium · Topic: Stress-Strain

Solution

Y = FL/(AΔL) = 400×2/(2×10⁻⁶×10⁻³) = 800/(2×10⁻⁹) = 4×10¹¹ N/m².

Q7. A wire of length 2 m, area 1 mm² is stretched 0.5 mm by force 100 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL) = 100×2/(1e-06×0.0005) = 4.00e+11 N/m².

Q8. A wire of length 1 m, area 2 mm² is stretched 0.1 mm by force 200 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL) = 200×1/(2e-06×0.0001) = 1.00e+12 N/m².

Q9. A wire of length 3 m, area 1 mm² is stretched 0.3 mm by force 500 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL) = 500×3/(1e-06×0.0003) = 5.00e+12 N/m².

Q10. A wire of length 2 m, area 2 mm² is stretched 0.25 mm by force 1000 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL) = 1000×2/(2e-06×0.00025) = 4.00e+12 N/m².

Q11. A wire of length 1 m, area 1 mm² is stretched 0.2 mm by force 400 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL) = 400×1/(1e-06×0.0002) = 2.00e+12 N/m².

Q12. A wire of length 1 m, area 1 mm² stretches by 0.5 mm under 100 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q13. A wire of length 2 m, area 2 mm² stretches by 0.6 mm under 200 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q14. A wire of length 3 m, area 3 mm² stretches by 0.7 mm under 300 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q15. A wire of length 4 m, area 4 mm² stretches by 0.8 mm under 400 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q16. A wire of length 5 m, area 5 mm² stretches by 0.9 mm under 500 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q17. A wire of length 6 m, area 6 mm² stretches by 1.0 mm under 600 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q18. A wire of length 7 m, area 7 mm² stretches by 1.1 mm under 700 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q19. A wire of length 8 m, area 8 mm² stretches by 1.2 mm under 800 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q20. A wire of length 9 m, area 9 mm² stretches by 1.3 mm under 900 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q21. A wire of length 10 m, area 10 mm² stretches by 1.4 mm under 1000 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q22. A wire of length 11 m, area 11 mm² stretches by 1.5 mm under 1100 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q23. A wire of length 12 m, area 12 mm² stretches by 1.6 mm under 1200 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q24. A wire of length 13 m, area 13 mm² stretches by 1.7 mm under 1300 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q25. A wire of length 14 m, area 14 mm² stretches by 1.8 mm under 1400 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q26. A wire of length 15 m, area 15 mm² stretches by 1.9 mm under 1500 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q27. A wire of length 16 m, area 16 mm² stretches by 2.0 mm under 1600 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q28. A wire of length 17 m, area 17 mm² stretches by 2.1 mm under 1700 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q29. A wire of length 18 m, area 18 mm² stretches by 2.2 mm under 1800 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q30. A wire of length 19 m, area 19 mm² stretches by 2.3 mm under 1900 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q31. A wire of length 20 m, area 20 mm² stretches by 2.4 mm under 2000 N. Young's modulus is:

Difficulty: Medium · Topic: Young's Modulus

Solution

Y = FL/(AΔL).

Q32. Wire: F=50N, L=1m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q33. Wire: F=50N, L=1m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q34. Wire: F=50N, L=1m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q35. Wire: F=50N, L=1m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q36. Wire: F=50N, L=1m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q37. Wire: F=50N, L=1m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.25e+11 Pa.

Q38. Wire: F=50N, L=1m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q39. Wire: F=50N, L=1m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+10 Pa.

Q40. Wire: F=50N, L=1m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.25e+11 Pa.

Q41. Wire: F=50N, L=1m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=6.25e+10 Pa.

Q42. Wire: F=50N, L=1m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+10 Pa.

Q43. Wire: F=50N, L=1m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.25e+10 Pa.

Q44. Wire: F=50N, L=2m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+12 Pa.

Q45. Wire: F=50N, L=2m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q46. Wire: F=50N, L=2m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+11 Pa.

Q47. Wire: F=50N, L=2m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q48. Wire: F=50N, L=2m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q49. Wire: F=50N, L=2m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q50. Wire: F=50N, L=2m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q51. Wire: F=50N, L=2m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q52. Wire: F=50N, L=2m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q53. Wire: F=50N, L=2m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.25e+11 Pa.

Q54. Wire: F=50N, L=2m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q55. Wire: F=50N, L=2m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+10 Pa.

Q56. Wire: F=50N, L=3m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+12 Pa.

Q57. Wire: F=50N, L=3m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+11 Pa.

Q58. Wire: F=50N, L=3m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.00e+11 Pa.

Q59. Wire: F=50N, L=3m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+11 Pa.

Q60. Wire: F=50N, L=3m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+11 Pa.

Q61. Wire: F=50N, L=3m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.75e+11 Pa.

Q62. Wire: F=50N, L=3m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+11 Pa.

Q63. Wire: F=50N, L=3m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+10 Pa.

Q64. Wire: F=50N, L=3m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.75e+11 Pa.

Q65. Wire: F=50N, L=3m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.88e+11 Pa.

Q66. Wire: F=50N, L=3m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+10 Pa.

Q67. Wire: F=50N, L=3m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.75e+10 Pa.

Q68. Wire: F=100N, L=1m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+12 Pa.

Q69. Wire: F=100N, L=1m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q70. Wire: F=100N, L=1m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+11 Pa.

Q71. Wire: F=100N, L=1m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q72. Wire: F=100N, L=1m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q73. Wire: F=100N, L=1m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q74. Wire: F=100N, L=1m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q75. Wire: F=100N, L=1m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q76. Wire: F=100N, L=1m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q77. Wire: F=100N, L=1m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.25e+11 Pa.

Q78. Wire: F=100N, L=1m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q79. Wire: F=100N, L=1m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+10 Pa.

Q80. Wire: F=100N, L=2m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+12 Pa.

Q81. Wire: F=100N, L=2m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+12 Pa.

Q82. Wire: F=100N, L=2m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=4.00e+11 Pa.

Q83. Wire: F=100N, L=2m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+11 Pa.

Q84. Wire: F=100N, L=2m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+12 Pa.

Q85. Wire: F=100N, L=2m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q86. Wire: F=100N, L=2m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+11 Pa.

Q87. Wire: F=100N, L=2m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q88. Wire: F=100N, L=2m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+11 Pa.

Q89. Wire: F=100N, L=2m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.50e+11 Pa.

Q90. Wire: F=100N, L=2m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.00e+11 Pa.

Q91. Wire: F=100N, L=2m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=5.00e+10 Pa.

Q92. Wire: F=100N, L=3m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.00e+12 Pa.

Q93. Wire: F=100N, L=3m, A=1mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+12 Pa.

Q94. Wire: F=100N, L=3m, A=1mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=6.00e+11 Pa.

Q95. Wire: F=100N, L=3m, A=1mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.00e+11 Pa.

Q96. Wire: F=100N, L=3m, A=2mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+12 Pa.

Q97. Wire: F=100N, L=3m, A=2mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+11 Pa.

Q98. Wire: F=100N, L=3m, A=2mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.00e+11 Pa.

Q99. Wire: F=100N, L=3m, A=2mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+11 Pa.

Q100. Wire: F=100N, L=3m, A=4mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+11 Pa.

Q101. Wire: F=100N, L=3m, A=4mm², ΔL=0.2mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=3.75e+11 Pa.

Q102. Wire: F=100N, L=3m, A=4mm², ΔL=0.5mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=1.50e+11 Pa.

Q103. Wire: F=100N, L=3m, A=4mm², ΔL=1.0mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=7.50e+10 Pa.

Q104. Wire: F=200N, L=1m, A=1mm², ΔL=0.1mm. Y=

Difficulty: Medium · Topic: Young's Modulus

Solution

Y=FL/AΔL=2.00e+12 Pa.

Other Chapters in Physics

Ch 1: Physical World Ch 2: Units & Measurements Ch 3: Motion in a Straight Line Ch 4: Motion in a Plane Ch 5: Laws of Motion Ch 6: Work Energy & Power Ch 7: System of Particles Ch 8: Gravitation Ch 10: Mechanical Properties of Fluids Ch 11: Thermal Properties of Matter Ch 12: Thermodynamics Ch 13: Kinetic Theory Ch 14: Oscillations Ch 15: Waves

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