Verified Solution • 2025–26 Session moderate

Q8.6: NCERT Physics - Part 2 MECHANICAL PROPERTIES OF SOLIDS 8.6 Solution: The edge of an aluminium cube is 10 cm long. One face of the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the loaded cube as a cantilever beam and apply the bending formula $\delta=FL^3/(3EI)$, which vastly overestimates the displacement. For a pure shear situation the correct relation is $\Delta =\frac{F L}{A G}$, using the shear modulus $G$ and the face area $A$, not the Young's modulus $E$.

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

Step-by-Step Verified Solution

**Answer:** Vertical deflection = 3.92×10−73.92 \times 10^{-7} m **Step-by-Step Explanation:** Given: Side L=0.1L = 0.1 m, Area A=(0.1)2=0.01A = (0.1)^2 = 0.01 m_, Force F=100×9.8=980F = 100 \times 9.8 = 980 N, Shear modulus G=25×109G = 25 \times 10^9 Pa. Shear stress = F/A=980/0.01=9.8×104F/A = 980/0.01 = 9.8 \times 10^4 Pa. Shear strain = Shear stress / G = 9.8×104/(25×109)=3.92×10−69.8 \times 10^4 / (25 \times 10^9) = 3.92 \times 10^{-6}. Vertical deflection Δx=Shear strain×L=3.92×10−6×0.1=3.92×10−7\Delta x = \text{Shear strain} \times L = 3.92 \times 10^{-6} \times 0.1 = 3.92 \times 10^{-7} m [citation:36].

All Questions in this Chapter

Q8.1 Q8.2 Q8.3 Q8.4 Q8.5 Q8.6 Q8.7 Q8.8 Q8.9 Q8.10 Q8.11 Q8.12 Q8.13 Q8.14 Q8.15 Q8.16

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from MECHANICAL PROPERTIES OF SOLIDS
Reference Textbook Solutions
Explore complete chapter exercises for NCERT Physics - Part 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring