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One end of a horizontal thick copper wir...

One end of a horizontal thick copper wire of length 2 L 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, find the ratio of the elongation in the thin wire to that in the thick wire.

Text Solution

Verified by Experts

Let the elongation produced in wire MN be `l_1` and that in PQ be `l_2`.

Since both the wires are made of copper, Young.s moduli will be same for both.
`therefore` From `Y=(FL)/(Al)` we have ,
`(F/(pi(2R)^2))/(l_2/(2L))=(F/(piR^2))/(l_1/L)`
or,`(2FL)/(4piR^2l_2)=(FL)/(piR^2l_1)`
or,`l_1/l_2=2`
`thereforel_1:l_2=2:1`
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