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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

A cube of aluminium of side 6cm is subjected to a tangential force...

A cube of aluminium of side 6cm6cm is subjected to a tangential force such that the top face is shears through 0.012cm0.012\text{cm} relative to the bottom face. The tangential force is k×1010dynek \times {10}^{10}dyne. What is the value of kk? [Shear modulus of the material is η=2×1011dynecm−2η = 2 \times {10}^{11}dyne{cm}^{- 2}]

Correct answer

1.44

Step-by-step solution

Lateral displacement, x=0.012cmx = 0 . 012cm

∴∴ Shearing strain,

θ=xL=0.0126=0.002\theta = \dfrac{x}{L} = \dfrac{0 . 012}{6} = 0 . 002

Shearing stress, Fa=ηθ\dfrac{F}{a} = η\theta

=2×1011×0.002= 2 \times {10}^{11} \times 0 . 002

=4×108dynecm−2= 4 \times {10}^{8}{dynecm}^{- 2}

Shearing force, F=F = shearing stress ×\times area

=4×108×(L)2= 4 \times {10}^{8} \times ( L{)}^{2}

=4×108×(6)2= 4 \times {10}^{8} \times ( 6{)}^{2}

=1.44×1010dyne= 1 . 44 \times {10}^{10}dyne

⇒K=1.44⇒ K = 1 . 44

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