First slide

Elastic Modulie

Question

A copper wire (Y = 10¹¹ Nm^-2) of length 8 m and a steel wire (Y = 2 X 10¹¹ Nm^-2) of length 4 m, each
of 0.5 cm² cross-section are fastened end-to-end and stretched with a tension of 500 N. Choose the
correct statement.

Moderate

A

Elongation in copper wire is 0.8 mm.
B

Elongation in steel is ¼.th the elongation in copper wire.
C

Total elongation is 1.0 mm.
D

All of the above

Solution

Elongation in the copper wire,
$(Δ l)_{C} = {(\frac{F l}{A Y})}_{C} = \frac{500 \times 8}{0.5 \times 10^{- 4} \times 10^{11}}$
$= 0.8 \times 10^{- 3} m = 0.8 mm$
Elongation in the steel wire,
$(Δ l)_{S} = {(\frac{F l}{A Y})}_{S} = \frac{500 \times 4}{0.5 \times 10^{- 4} \times 2 \times 10^{11}}$
$= 0.2 \times 10^{- 3} m = 0.2 mm$
$(Δ l)_{S} = \frac{1}{4} (Δ l)_{C}$
and total elongation, $Δ l$ = 0.8 + 0.2= 1.0 mm

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