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Young’s modul...

Question

Young’s moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R$ . Wire $B$ is $1.5 m$ long and has radius $2 m m$ . If the two wires stretch by the same length for a given load, then the value of $R$ is close to

A

1.3 m m

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B

1.9 m m

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C

1.5 m m

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D

1.7 m m

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Solution

The correct option is D $1.7 m m$
Formula used: $\frac{Δ l}{l} = \frac{F}{A Y}$

Given: $\frac{Y_{A}}{Y_{B}} = \frac{7}{4}, L_{A} = 2 m, A_{A} = π R^{2}, L_{B} = 1.5 m, r_{B} = 2 m m$

$\frac{F}{l} = Y (\frac{A}{L})$

given $F$ and $l$ are same, $\frac{A Y}{L}$ is same

$\frac{A_{A} Y_{A}}{L_{A}} = \frac{A_{B} Y_{B}}{L_{B}}$

$\frac{(π R^{2}) (\frac{7}{4} Y_{B})}{2} = \frac{π (2)^{2} \cdot Y_{B}}{1.5}$

$R = 1.74 m m$
FINAL ANSWER: (b)

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