Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a: b. Then a/b can be expressed as 1 / x where x is.

Question

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a: b. Then a/b can be expressed as 1 / x where x is. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For A ( E /π r 2)= y (2 mm / a ) ......(1) For B ( E /π ⋅ 16 r 2)= y (4 mm / b ) .......(2) ∴ (1) (2) 16=(2 b /4 a ) (a/b)=(1/32) ∴ Answer =32

For A πr2E​=ya2mm​......(1) For Bπ⋅16r2E​=yb4mm​.......(2) ∴(1)(2) 16=4a2b​ ba​=321​ ∴ Answer =32

For A $\frac{E}{π r ^{2}} = y \frac{2 mm}{a} ...... (1)$
For $B \frac{E}{π \cdot 16 r ^{2}} = y \frac{4 mm}{b} ....... (2)$
$∴ (1) (2)$
$16 = \frac{2 b}{4 a}$
$\frac{a}{b} = \frac{1}{32}$
$∴$ Answer $= 32$