A wire is stretched by 1 mm by a force of 1 kN. How long would a wire of same material and length but of four times radius be stretched by same force.

Question

A wire is stretched by 1 mm by a force of 1 kN. How long would a wire of same material and length but of four times radius be stretched by same force. (A) (1/2) mm (B) (1/4) mm (C) (1/8) mm (D) (1/16) mm

Tardigrade Admin · Accepted Answer

(F/a)=Y ⋅ (Δ L/L) Δ L=(F L/Y a) ∴ Δ L propto (1/a)(F, Y= const. ) (Δ L'/Δ L)=(a/a')=[(π r2/π(4 r)2)] =(1/16) mm

Q. A wire is stretched by $1 mm$ by a force of $1 k N$ . How long would a wire of same material and length but of four times radius be stretched by same force.

$\frac{1}{2} mm$

$\frac{1}{4} mm$

$\frac{1}{8} mm$

$\frac{1}{16} mm$

$\frac{F}{a} = Y \cdot \frac{Δ L}{L}$
$Δ L = \frac{F L}{Ya}$
$∴ Δ L \propto \frac{1}{a} (F, Y =$ const. $)$
$\frac{Δ L ^{'}}{Δ L} = \frac{a}{a ^{'}} = [\frac{π r ^{2}}{π ( 4 r ) ^{2}}]$
$= \frac{1}{16} mm$

Q. A wire is stretched by 1mm by a force of 1kN. How long would a wire of same material and length but of four times radius be stretched by same force.

21​mm

41​mm

81​mm

161​mm