Two wires A and B of same length and made of same material are hanging from the same roof. The figure shows the load F versus extension $Δ l$ graph for the two wires then:

Question

Smart Achievers · Accepted Answer

(3)

$As seen from graph, Δ ℓ_{A} = Δ ℓ_{B} \Rightarrow \frac{F_{A} L_{A}}{π r_{A}^{2} Y_{A}} = \frac{F_{B} L_{B}}{π r_{B}^{2} Y_{B}} \Rightarrow \frac{10 \times L}{π r_{A}^{2} \times Y} = \frac{40 \times L}{π r_{B}^{2} \times Y} \Rightarrow \frac{r_{A}}{r_{B}} = \frac{1}{2}$

Solution

Q.
Two wires A and B of same length and made of same material are hanging from the same roof. The figure shows the load F versus extension $Δ l$ graph for the two wires then:

1 The elasticity of wire A is greater than that of B

2 The cross-sectional area of wire A is equal to that of B

3 The ratio of radii of wires A to B is 1 : 2

4 The ratio of area of cross-section of wires A to B is 4 : 1

Ans.
(3)

$As seen from graph, Δ ℓ_{A} = Δ ℓ_{B} \Rightarrow \frac{F_{A} L_{A}}{π r_{A}^{2} Y_{A}} = \frac{F_{B} L_{B}}{π r_{B}^{2} Y_{B}} \Rightarrow \frac{10 \times L}{π r_{A}^{2} \times Y} = \frac{40 \times L}{π r_{B}^{2} \times Y} \Rightarrow \frac{r_{A}}{r_{B}} = \frac{1}{2}$

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