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A 5m aluminium wire (Y = 7 xx 10^(10) Nm...

A 5m aluminium wire `(Y = 7 xx 10^(10) Nm^(-2)`) of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire `(Y = 12 xx 10^(10) Nm^(-2)`) of the same length under the same weight, the diameter (in mm) should be

A

1.75

B

1.5

C

2.5

D

`5.0`

Text Solution

Verified by Experts

The correct Answer is:
C
`(Delta l_(Al))/(Delta l_(Cu))= (F_(Al) l_(Al))/(Y_(Al)A_(Al)) xx (Y_(Cu) A_(Cu))/(F_(Cu) xx l_(Cu))`
`= ((12 xx 10^(10))/(7 xx 10^(10))) ((d_(Cu))/(d_(Al)))^(2)`
`rArr (d_(Cu))/(d_(Al)) = ((7)/(12))^(1//2)`
`rArr d_(Cu)= 2.29`mm (Approx)
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