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A rubber eraser with dimensions 2 cm x 4 cm x 8 cm is fixed to a horizontal surface at its base (the 2 cm x 4 cm face), with the 4 cm edge oriented vertically. A horizontal force of 16 N is applied to the top face. What is the shear strain developed? (Shear modulus of rubber G = 1.5 x 10⁵ N/m²)
- 2/15
- 1/15
- 1/30
- 1/60
Correct answer: 1/15
Solution
The eraser stands with the 4 cm edge vertical, so the base is 2 cm x 8 cm = 16 cm² = 16 x 10⁻⁴ m². Shear stress tau = 16 / (16 x 10⁻⁴) = 10⁴ Pa. Shear strain = tau/G = 10⁴ / (1.5 x 10⁵) = 1/15.
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