A wire of cross section 4 mm is stretched by 0.1 mm by a certain weight. How far (length) will be wire of same material and length but of area `8 mm` stretch under the action of same force.

Options

A. 0.05mm
B. 0.10mm
C. 0.15mm
D. 0.20mm

Answer

A

Explanation

Here, `A_(1) =4mm^(2) = 4 xx 10^(-6) m^(2), Delta L_(1) = 0.1 xx 10^(-3) m`
`A_(2) = 8mm^(2) = 8 xx 10^(-6) m^(2), Y_(2) = Y_(1), L_(2) = L_(1), F_(2) = F_(1), Delta L_(2) = ?`
`Delta L_(1) = (F_(1) L_(1))/(A_(1) Y_(1)), Delta L_(2) = (F_(2) L_(2))/(A_(2) Y_(2))`
`:. (Delta L_(2))/(Delta L_(1)) = (A_(1))/(A_(2)) = (4 xx 10^(-6))/(8 xx 10^(-6)) = (1)/(2)`
or `Delta L_(2) = (Delta L_(1))/(2) = 0.05 xx 10^(-3) m = 0.05mm`