Consider two elastic bands of equal cross-sectional area but one is twice as lon

Question

Consider two elastic bands of equal cross-sectional area but one is twice as long as the other. The same stress is applied to each elastic band. Which one of the following statements is correct?

a. The longer elastic band stretches four times as much as the shorter one.

b. The longer elastic band stretches twice as much as the shorter one.

c. Both elastic bands stretch by the same amount.

Consider a static fluid. Let P be the pressure of the fluid, let A be the area of a small surface of the fluid's container, and let F be the force of the fluid on the area A. Which one of the following statements is correct?

a. F = PA and the force is directed parallel to the surface.

b. F = PA and the force is directed perpendicular to the surface.    

c. F = P/A and the force is directed perpendicular to the surface

Explanation / Answer

since both the elastic bands are made of same material

Stress / strain for both will be the same

Stress = F/A which will be the same for both

Strain = l/L will be different

l1/L1 =l2 /L2

l1/l2 = 2L/L = 2

so the longer one streches twice as much as the shorter one

so option b is the correct answer

2) Force = Pressure /area and it acts perpendicular to the surface

so option c) F= P/A is the correct asnwer

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