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A wire of length L and radius a rigidly ...

A wire of length L and radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is L, if another wire of same material but of length 2 L and radius 2 a is stretched with a force 2 F, the increase in its length will be

Text Solution

Verified by Experts

The situation is shown in the diagram.
Now, Young's modulus (Y) `= (f)/(A) xx (L)/(l)`
For first wire, `" "Y = (f) /(pir^(2))xx(L)/(l)" .....(i)"`
For second wire, `" "Y = (2f)/(pi (2r)^(2))xx(2L)/(l')`
`" "=(f)/(pir^(2))xx(L)/(l' )" .....(ii)"`
From Eqs. (i) and (ii), `" "(f)/(pir^(2))xx(L)/(l)=(f)/(pir^(2))xx(L)/(l')`
`therefore " " (because "Both wires are of same material, hence, Young's modulus will be same")`.
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