PhysicsThe 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. Then is the vertical deflection of this face

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. Then is the vertical deflection of this face

  1. A

    3×10-7m

  2. B

    4×10-7m

  3. C

    8×10-7m

  4. D

    2×10-7m

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    Solution:

    The vertical deflection of the face can be calculated as follows:Shear stress= Shear force Area of the face Shear force

    Shear stress =100kg×9.8m/s2(mass× acceleration due to gravity)

    Area of the face = (10cm)2=0.01m2

    Shear stress=100kg×9.8m/s20.01m2=98000Pa

    Shear strain = Shear stressShear modulus

     Shear strain = 98,000 Pa25 GPa= 3.92×10-7m

    .Shear strain  4×10-7m

    Hence the correct answer is 4×10-7m.

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