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Shear modulus: displacement or angle of the upper face of a block under a shearing force

This type of question, asked 3 times: 27 Jul 2022, 4 Apr 2025, 5 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    28
    A square aluminium (shear modulus is 25×109Nm−225 \times10^{9}Nm^{- 2} ) slab of side 60 cm60\text{ }cm and thickness 15 cm15\text{ }cm is subjected to a shearing force (on its narrow face) of 18.0×104 N18.0 \times10^{4}\text{ }N. The lower edge is riveted to the floor. The displacement of the upper edge is ____ μm\_\_\_\_\ \mu m.

  2. Question 2

    4 Apr 2025

    22
    Two slabs with square cross section of different materials (1,2)(1,2) with equal sides (l)(l) and thickness d1d_{1} and d2d_{2} such that d2=2 d1d_{2} = 2{\text{ }d}_{1} and l>d2l > d_{2}. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is θ2=2θ1\theta_{2} = 2\theta_{1}. If the shear modulus of material 1 is 4×109 N/m24 \times 10^{9}\text{ }N/m^{2}, then the shear modulus of material 2 is x×109 N/m2x \times 10^{9}\text{ }N/m^{2}, where the value of xx is ____\_\_\_\_.

  3. Question 3

    4 Apr 2025

    80
    A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 105 N10^{5}\text{ }N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement θ\theta of the rod axis from its original position would be : (shear moduli, G=1010 N/m2G =10^{10}\text{ }N/m^{2} )

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  4. Question 4

    5 Apr 2026 S1

    21
    A cube has side length 5 cm and modulus of rigidity 105 N/m210^{5}\text{ }N/m^{2}. The displacement produced by a force of 10 N in the upper face of cube is ____\_\_\_\_ mm .