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When the tension in a metal wire is T(1)...

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

A

`(L_(1) + L_(2))/(2)`

B

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

C

`sqrt((L_(1)L_(2))/(2))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`T_(1) = K[L_(1) - L], T_(2) = K[L_(2) - L]`
`:. (T_(2))/(T_(1)) = (L_(2) - L)/(L_(1) - L)`
`:. T_(2)L_(1) - T_(2)L = T_(1)L_(2) - T_(1)L`
`:. T_(2)L_(1) - T_(1)L_(2) = (T_(2) - T_(1))L`
`:. L = (T_(2) L_(1) - T_(1)L_(2))/(T_(2) - T_(1))`
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