Question

A wire has a cross sectional area of 4.00 mm2 and is stretched by 0.100 mm by a certain force. How far will a wire of the same material and length stretch if its cross-sectional area is 8.00 mm2 and the same force is used to stretch it

Answer 1

Answer:
`0.05\ mm`

Step-by-step explanation:

Given

Cross-sectional area of wire
`A_1=4\ mm^2`

Extension of wire
`\delta l=0.1\ mm`

Extension in a wire is given by

`\Rightarrow \delta l=(FL)/(AE)`

where,
`E=\text{Youngs modulus}`

`\Rightarrow \delta_1=(FL)/(A_1E)\quad \ldots(i)`

for same force, length and material

`\Rightarrow \delta_2=(FL)/(A_2E)\quad \ldots(ii)`

Divide (i) and (ii)

`\Rightarrow (0.1)/(\delta_2)=(A_2)/(A_1)\\\\\Rightarrow \delta_2=0.1* (4)/(8)\\\\\Rightarrow \delta_2=0.05\ mm`