Four wires of the same material are stretched by the same load. The dimension of the wires are as given below. The one which has the maximum elongation is of
Text Solution
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The elongation of a wire under a load is given by the formula:
where 
is the elongation, F is the force applied, L is the original length, A is the cross-sectional area, and Y is Young's modulus of the material. Since the wires are made of the same material and are stretched by the same load. Young's modulus Y and the force F are constants. Therefore, the elongation depends on the ratio 
. The cross-sectional area A of a wire with diameter d is given by 
. Thus. the elongation formula can be rewritten as:
We need to calculate this ratio for each wire to determine which one elongates the most.
Step by Step Solution:
Calculate the ratio 
for wire :
Calculate the ratio 
for wire :
Calculate the ratio 
for wire :
Calculate the ratio 
for wire :
Compare the ratios: The wire with the highest ratio 
will elongate the most. Wire has the highest ratio of 2 \times 10 6 .
The wire with length 0.5 m and diameter 0.5 mm elongates the most.
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