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Four wires of the same material but havi...

Four wires of the same material but having different lentghs and radii are subjected to same load. Which of the following combinations of length L and radius r will have the heighest elongation ?

A

L = 200 cm, r = 2mm

B

L = 300cm, r = 3mm

C

L = 400 cm, r = 4mm

D

L = 100 cm, r = 1mm

Text Solution

Verified by Experts

The correct Answer is:
D
`e = (M gL)/(pi r^(2)Y)`
Thus for same Y and Mg, elongation `prop (L)/(r^(2))`
Then, `e_(1) prop (200)/(2^(2))` or `prop (200)/(4), e_(2) prop (300)/(9)`
`e_(3) prop (400)/(16)` and `e_(4) prop (100)/(1^(2))`
Thus `e_(4)` is maximum or wire D has the highest elongation.
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