One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the

Question

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is [2013]

Smart Achievers · Accepted Answer

(3)

$Using, Y = \frac{F / A}{Δ ℓ / ℓ_{0}}$

$Y = \frac{F / π {(2 R)}^{2}}{Δ ℓ_{1} / 2 L} = \frac{F / π R^{2}}{Δ ℓ_{2} / L}$

$∴$ $\frac{Δ ℓ_{2}}{Δ ℓ_{1}} = 2$

Solution

1 0.25

2 0.50

3 2.00

4 4.00

Ans.
(3)

$Using, Y = \frac{F / A}{Δ ℓ / ℓ_{0}}$

$Y = \frac{F / π {(2 R)}^{2}}{Δ ℓ_{1} / 2 L} = \frac{F / π R^{2}}{Δ ℓ_{2} / L}$

$∴$ $\frac{Δ ℓ_{2}}{Δ ℓ_{1}} = 2$

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