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The length of a steel wire is l(1) when ...

The length of a steel wire is `l_(1)` when the stretching force is `T_(1)` and `l_(2)` when the stretching force is `T_(2)`. The natural length of the wire is

A

`(l_(1)T_(1)+l_(2)T_(2))/(T_(1)+T_(2))`

B

`(l_(2)T_(1)+l_(1)T_(2))/(T_(1)+T_(2))`

C

`(l_(2)T_(1)-l_(1)T_(2))/(T_(1)-T_(2))`

D

`(l_(1)T_(1)-l_(2)T_(2))/(T_(1)-T_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`l_(1) -l = (T_(1)l)/(AY)` …(i)
` l_(2)-l = (T_(2)l)/(AY)` …..(iii)
Dividing Eq. (i) by Eq. (ii) and then simplifying , We get
`l = (l_(2)T_(1) -l_(1)T_(2))/(T_(1) -T_(2))`
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Knowledge Check

  • The length of a metal wire is l_(1) when the tension in it is T_(1) and is l_(2) when the tension is T_(2) . Then natural length of the wire is

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  • When the tension in a metal wire is T_(1) , its length is I_(1) . When the tension is T_(2) , its length is I_(2) . The natural length of wire is

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