One face CD of a brass cube ABCD having length of side $$10$$ cm is fixed and a tangential force is applied on the free face A. As a result the angular displacement of the other face is $$0.18o$$. If shear modulus of brass is $$4$$×$$1010$$ $$N/m2$$, the elastic potential energy stored in the cube is π$$2$$≈$$10$$

Question

One face CD of a brass cube ABCD having length of side $$10$$ cm is fixed and a tangential force is applied on the free face A. As a result the angular displacement of the other face is $$0.18o$$. If shear modulus of brass is $$4$$×$$1010$$ $$N/m2$$, the elastic potential energy stored in the cube is π$$2$$≈$$10$$

Infinity Learn · Accepted Answer

Shear strain, θ$$=0.18o=$$π$$180$$×$$0.18$$​$$rad=$$π$$1000rad$$∴ strain energy stored per unit $$volumeu=12$$ηθ$$2=12$$×$$4$$×$$1010$$×π$$10002$$ $$Jm3=2$$×$$1010$$×$$10106$$ $$Jm3=2$$×$$105$$ $$Jm3$$∴Total strain energy stored $$=$$ volume x energy density $$=101003$$×$$2$$×$$105J=200$$ J

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One face CD of a brass cube ABCD having length of side 10 cm is fixed and a tangential force is applied on the free face A. As a result the angular displacement of the other face is 0.18o. If shear modulus of brass is 4×1010 N/m2, the elastic potential energy stored in the cube is π2≈10

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