The base of a metal block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060 . The shear modulus of this metal is $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$ The displacement of the upper face, in the direction of the applied force is closest to
A) 5.4 mm
B) 4.8 mm
C) 3.0 mm
D) 4.2 mm
E) 3.6 mm

Question

The base of a metal block, which is fixed in place, measures  90 cm by  90 cm, and the height of the block is  60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of  0.0060 . The shear modulus of this metal is $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$ The displacement of the upper face, in the direction of the applied force is closest to
A)  5.4 mm
B)  4.8 mm
C)  3.0 mm
D)  4.2 mm
E)  3.6 mm

Quizplus · Accepted Answer

The displacement can be calculated using the formula for shear strain: $\text{shear strain} = \frac{\text{displacement}}{\text{height}}$. Given the shear strain is 0.0060 and the height is 60 cm (or 600 mm), the displacement is $0.0060 \times 600 \, \text{mm} = 3.6 \, \text{mm}$.

The Base of a Metal Block, Which Is Fixed in Place